Adaptive synchrosqueezing based on a quilted short-time Fourier transform

NASA Astrophysics Data System (ADS)

Berrian, Alexander; Saito, Naoki

2017-08-01

In recent years, the synchrosqueezing transform (SST) has gained popularity as a method for the analysis of signals that can be broken down into multiple components determined by instantaneous amplitudes and phases. One such version of SST, based on the short-time Fourier transform (STFT), enables the sharpening of instantaneous frequency (IF) information derived from the STFT, as well as the separation of amplitude-phase components corresponding to distinct IF curves. However, this SST is limited by the time-frequency resolution of the underlying window function, and may not resolve signals exhibiting diverse time-frequency behaviors with sufficient accuracy. In this work, we develop a framework for an SST based on a "quilted" short-time Fourier transform (SST-QSTFT), which allows adaptation to signal behavior in separate time-frequency regions through the use of multiple windows. This motivates us to introduce a discrete reassignment frequency formula based on a finite difference of the phase spectrum, ensuring computational accuracy for a wider variety of windows. We develop a theoretical framework for the SST-QSTFT in both the continuous and the discrete settings, and describe an algorithm for the automatic selection of optimal windows depending on the region of interest. Using synthetic data, we demonstrate the superior numerical performance of SST-QSTFT relative to other SST methods in a noisy context. Finally, we apply SST-QSTFT to audio recordings of animal calls to demonstrate the potential of our method for the analysis of real bioacoustic signals.

Absorption Mode FT-ICR Mass Spectrometry Imaging

DOE Office of Scientific and Technical Information (OSTI.GOV)

Smith, Donald F.; Kilgour, David P.; Konijnenburg, Marco

2013-12-03

Fourier transform ion cyclotron resonance mass spectrometry offers the highest mass resolving power for molecular imaging experiments. This high mass resolving power ensures that closely spaced peaks at the same nominal mass are resolved for proper image generation. Typically higher magnetic fields are used to increase mass resolving power. However, a gain in mass resolving power can also be realized by phase correction of the data for absorption mode display. In addition to mass resolving power, absorption mode offers higher mass accuracy and signal-to-noise ratio over the conventional magnitude mode. Here we present the first use of absorption mode formore » Fourier transform ion cyclotron resonance mass spectrometry imaging. The Autophaser algorithm is used to phase correct each spectrum (pixel) in the image and then these parameters are used by the Chameleon work-flow based data processing software to generate absorption mode ?Datacubes? for image and spectral viewing. Absorption mode reveals new mass and spatial features that are not resolved in magnitude mode and results in improved selected ion image contrast.« less

Implementation of Time-Resolved Step-Scan Fourier Transform Infrared (FT-IR) Spectroscopy Using a kHz Repetition Rate Pump Laser

PubMed Central

MAGANA, DONNY; PARUL, DZMITRY; DYER, R. BRIAN; SHREVE, ANDREW P.

2011-01-01

Time-resolved step-scan Fourier transform infrared (FT-IR) spectroscopy has been shown to be invaluable for studying excited-state structures and dynamics in both biological and inorganic systems. Despite the established utility of this method, technical challenges continue to limit the data quality and more wide ranging applications. A critical problem has been the low laser repetition rate and interferometer stepping rate (both are typically 10 Hz) used for data acquisition. Here we demonstrate significant improvement in the quality of time-resolved spectra through the use of a kHz repetition rate laser to achieve kHz excitation and data collection rates while stepping the spectrometer at 200 Hz. We have studied the metal-to-ligand charge transfer excited state of Ru(bipyridine)3Cl2 in deuterated acetonitrile to test and optimize high repetition rate data collection. Comparison of different interferometer stepping rates reveals an optimum rate of 200 Hz due to minimization of long-term baseline drift. With the improved collection efficiency and signal-to-noise ratio, better assignments of the MLCT excited-state bands can be made. Using optimized parameters, carbonmonoxy myoglobin in deuterated buffer is also studied by observing the infrared signatures of carbon monoxide photolysis upon excitation of the heme. We conclude from these studies that a substantial increase in performance of ss-FT-IR instrumentation is achieved by coupling commercial infrared benches with kHz repetition rate lasers. PMID:21513597

Improving Thin Bed Identification in Sarawak Basin Field using Short Time Fourier Transform Half Cepstrum (STFTHC) method

NASA Astrophysics Data System (ADS)

Nizarul, O.; Hermana, M.; Bashir, Y.; Ghosh, D. P.

2016-02-01

In delineating complex subsurface geological feature, broad band of frequencies are needed to unveil the often hidden features of hydrocarbon basin such as thin bedding. The ability to resolve thin geological horizon on seismic data is recognized to be a fundamental importance for hydrocarbon exploration, seismic interpretation and reserve prediction. For thin bedding, high frequency content is needed to enable tuning, which can be done by applying the band width extension technique. This paper shows an application of Short Time Fourier Transform Half Cepstrum (STFTHC) method, a frequency bandwidth expansion technique for non-stationary seismic signal in increasing the temporal resolution to uncover thin beds and improve characterization of the basin. A wedge model and synthetic seismic data is used to quantify the algorithm as well as real data from Sarawak basin were used to show the effectiveness of this method in enhancing the resolution.

Development of Imaging Fourier-Transform Spectroscopy for the Characterization of Turbulent Jet Flames

DTIC Science & Technology

2014-09-18

Spatially resolved infrared spectra of jet exhaust from an F109 turbofan engine...Appendix E contains a conference proceeding in its entirety [32]. This proceeding summarizes analysis of a turbofan engine exhaust via the Hyper-Cam and...demonstrated in a separate experiment. Recently, exhaust from an F109 turbofan engine was imaged with the IFTS[32]. Examination of the time-averaged

Time-Frequency Approach for Stochastic Signal Detection

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ghosh, Ripul; Akula, Aparna; Kumar, Satish

2011-10-20

The detection of events in a stochastic signal has been a subject of great interest. One of the oldest signal processing technique, Fourier Transform of a signal contains information regarding frequency content, but it cannot resolve the exact onset of changes in the frequency, all temporal information is contained in the phase of the transform. On the other hand, Spectrogram is better able to resolve temporal evolution of frequency content, but has a trade-off in time resolution versus frequency resolution in accordance with the uncertainty principle. Therefore, time-frequency representations are considered for energetic characterisation of the non-stationary signals. Wigner Villemore » Distribution (WVD) is the most prominent quadratic time-frequency signal representation and used for analysing frequency variations in signals.WVD allows for instantaneous frequency estimation at each data point, for a typical temporal resolution of fractions of a second. This paper through simulations describes the way time frequency models are applied for the detection of event in a stochastic signal.« less

Time-Frequency Approach for Stochastic Signal Detection

NASA Astrophysics Data System (ADS)

Ghosh, Ripul; Akula, Aparna; Kumar, Satish; Sardana, H. K.

2011-10-01

The detection of events in a stochastic signal has been a subject of great interest. One of the oldest signal processing technique, Fourier Transform of a signal contains information regarding frequency content, but it cannot resolve the exact onset of changes in the frequency, all temporal information is contained in the phase of the transform. On the other hand, Spectrogram is better able to resolve temporal evolution of frequency content, but has a trade-off in time resolution versus frequency resolution in accordance with the uncertainty principle. Therefore, time-frequency representations are considered for energetic characterisation of the non-stationary signals. Wigner Ville Distribution (WVD) is the most prominent quadratic time-frequency signal representation and used for analysing frequency variations in signals.WVD allows for instantaneous frequency estimation at each data point, for a typical temporal resolution of fractions of a second. This paper through simulations describes the way time frequency models are applied for the detection of event in a stochastic signal.

Unmixing the Materials and Mechanics Contributions in Non-resolved Object Signatures

DTIC Science & Technology

2008-09-01

abundances from hyperspectral or multi-spectral time - resolved signatures. A Fourier analysis of temporal variation of material abundance provides...factorization technique to extract the temporal variation of material abundances from hyperspectral or multi-spectral time - resolved signatures. A Fourier...approximately one hundred wavelengths in the visible spectrum. The frame rate for the instrument was not large enough to collect time resolved data. However

Analysis of photonic Doppler velocimetry data based on the continuous wavelet transform

DOE Office of Scientific and Technical Information (OSTI.GOV)

Liu Shouxian; Wang Detian; Li Tao

2011-02-15

The short time Fourier transform (STFT) cannot resolve rapid velocity changes in most photonic Doppler velocimetry (PDV) data. A practical analysis method based on the continuous wavelet transform (CWT) was presented to overcome this difficulty. The adaptability of the wavelet family predicates that the continuous wavelet transform uses an adaptive time window to estimate the instantaneous frequency of signals. The local frequencies of signal are accurately determined by finding the ridge in the spectrogram of the CWT and then are converted to target velocity according to the Doppler effects. A performance comparison between the CWT and STFT is demonstrated bymore » a plate-impact experiment data. The results illustrate that the new method is automatic and adequate for analysis of PDV data.« less

The Application of MP-FTS to Aperture Synthesis

NASA Astrophysics Data System (ADS)

Hattori, M.; Ohta, I. S.; Matsuo, H.; Shibata, Y.

2000-12-01

The application of the Martin-Puplett type Fourier transform spectrometer to aperture synthesis is considered. The configuration of the mirrors and beam splitters and the fundamental mathematical elements of the system are summarized. We show that the system can measure spectrally resolved spatial distribution of the Stokes parameters of sources as interfered signals. An original Martin-Puplett type Fourier transform spectrometer that can be applied to aperture synthesis in mm and sub-mm wave bands has been constructed. The preliminary results of our laboratory experiments are reported.

Time-resolved two-window measurement of Wigner functions for coherent backscatter from a turbid medium

NASA Astrophysics Data System (ADS)

Reil, Frank; Thomas, John E.

2002-05-01

For the first time we are able to observe the time-resolved Wigner function of enhanced backscatter from a random medium using a novel two-window technique. This technique enables us to directly verify the phase-conjugating properties of random media. An incident divergent beam displays a convergent enhanced backscatter cone. We measure the joint position and momentum (x, p) distributions of the light field as a function of propagation time in the medium. The two-window technique allows us to independently control the resolutions for position and momentum, thereby surpassing the uncertainty limit associated with Fourier transform pairs. By using a low-coherence light source in a heterodyne detection scheme, we observe enhanced backscattering resolved by path length in the random medium, providing information about the evolution of optical coherence as a function of penetration depth in the random medium.

Novel laser gain and time-resolved FTIR studies of photochemistry

NASA Technical Reports Server (NTRS)

Leone, Stephen R.

1990-01-01

Several techniques are discussed which can be used to explore laboratory photochemical processes and kinetics relevant to planetary atmospheres; these include time-resolved laser gain-versus-absorption spectroscopy and time-resolved Fourier transform infrared (FTIR) emission studies. The laser gain-versus-absorption method employed tunable diode and F-center lasers to determine the yields of excited photofragments and their kinetics. The time-resolved FTIR technique synchronizes the sweep of a commercial FTIR with a pulsed source of light to obtain emission spectra of novel transient species in the infrared. These methods are presently being employed to investigate molecular photodissociation, the yields of excited states of fragments, their subsequent reaction kinetics, Doppler velocity distributions, and velocity-changing collisions of translationally fast atoms. Such techniques may be employed in future investigations of planetary atmospheres, for example to study polycyclic aromatic hydrocarbons related to cometary emissions, to analyze acetylene decomposition products and reactions, and to determine spectral features in the near infrared and infrared wavelength regions for planetary molecules and clusters.

Research about vibration characteristics of timing chain system based on short-time Fourier transform

NASA Astrophysics Data System (ADS)

Xi, Jiaxin; Liu, Ning

2017-09-01

Vibration characteristic of timing chain system is very important for an engine. In this study, we used a bush roller chain drive system as an example to explain how to use mulitybody dynamic techniques and short-time Fourier transform to investigate vibration characteristics of timing chain system. Multibody dynamic simulation data as chain tension force and external excitation sources curves were provided for short-time Fourier transform study. The study results of short-time Fourier transform illustrate that there are two main vibration frequency domain of timing chain system, one is the low frequency vibration caused by crankshaft sprocket velocity and camshaft sprocket torque. Another is vibration around 1000Hz lead by hydraulic tensioner. Hence, short-time Fourier transform method is useful for basic research of vibration characteristics for timing chain system.

An optical Fourier transform coprocessor with direct phase determination.

PubMed

Macfaden, Alexander J; Gordon, George S D; Wilkinson, Timothy D

2017-10-20

The Fourier transform is a ubiquitous mathematical operation which arises naturally in optics. We propose and demonstrate a practical method to optically evaluate a complex-to-complex discrete Fourier transform. By implementing the Fourier transform optically we can overcome the limiting O(nlogn) complexity of fast Fourier transform algorithms. Efficiently extracting the phase from the well-known optical Fourier transform is challenging. By appropriately decomposing the input and exploiting symmetries of the Fourier transform we are able to determine the phase directly from straightforward intensity measurements, creating an optical Fourier transform with O(n) apparent complexity. Performing larger optical Fourier transforms requires higher resolution spatial light modulators, but the execution time remains unchanged. This method could unlock the potential of the optical Fourier transform to permit 2D complex-to-complex discrete Fourier transforms with a performance that is currently untenable, with applications across information processing and computational physics.

Big Data in Reciprocal Space: Sliding Fast Fourier Transforms for Determining Periodicity

DOE PAGES

Vasudevan, Rama K.; Belianinov, Alex; Gianfrancesco, Anthony G.; ...

2015-03-03

Significant advances in atomically resolved imaging of crystals and surfaces have occurred in the last decade allowing unprecedented insight into local crystal structures and periodicity. Yet, the analysis of the long-range periodicity from the local imaging data, critical to correlation of functional properties and chemistry to the local crystallography, remains a challenge. Here, we introduce a Sliding Fast Fourier Transform (FFT) filter to analyze atomically resolved images of in-situ grown La5/8Ca3/8MnO3 films. We demonstrate the ability of sliding FFT algorithm to differentiate two sub-lattices, resulting from a mixed-terminated surface. Principal Component Analysis (PCA) and Independent Component Analysis (ICA) of themore » Sliding FFT dataset reveal the distinct changes in crystallography, step edges and boundaries between the multiple sub-lattices. The method is universal for images with any periodicity, and is especially amenable to atomically resolved probe and electron-microscopy data for rapid identification of the sub-lattices present.« less

Big Data in Reciprocal Space: Sliding Fast Fourier Transforms for Determining Periodicity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Vasudevan, Rama K.; Belianinov, Alex; Gianfrancesco, Anthony G.

Significant advances in atomically resolved imaging of crystals and surfaces have occurred in the last decade allowing unprecedented insight into local crystal structures and periodicity. Yet, the analysis of the long-range periodicity from the local imaging data, critical to correlation of functional properties and chemistry to the local crystallography, remains a challenge. Here, we introduce a Sliding Fast Fourier Transform (FFT) filter to analyze atomically resolved images of in-situ grown La5/8Ca3/8MnO3 films. We demonstrate the ability of sliding FFT algorithm to differentiate two sub-lattices, resulting from a mixed-terminated surface. Principal Component Analysis (PCA) and Independent Component Analysis (ICA) of themore » Sliding FFT dataset reveal the distinct changes in crystallography, step edges and boundaries between the multiple sub-lattices. The method is universal for images with any periodicity, and is especially amenable to atomically resolved probe and electron-microscopy data for rapid identification of the sub-lattices present.« less

Spatiotemporal characterization of ultrashort optical vortex pulses

NASA Astrophysics Data System (ADS)

Miranda, Miguel; Kotur, Marija; Rudawski, Piotr; Guo, Chen; Harth, Anne; L'Huillier, Anne; Arnold, Cord L.

2017-12-01

We use a spiral phase plate to generate few-cycle optical vortices from an ultrafast titanium:sapphire oscillator and characterize them in the spatiotemporal domain with a recently introduced technique based on spatially resolved Fourier transform spectrometry. The performance of this simple approach to the generation of optical vortices is analysed from a wavelength-dependent perspective as well as in the spatiotemporal domain, allowing us to characterize ultrashort vortex pulses in space, frequency and time.

A fast algorithm for vertex-frequency representations of signals on graphs

PubMed Central

Jestrović, Iva; Coyle, James L.; Sejdić, Ervin

2016-01-01

The windowed Fourier transform (short time Fourier transform) and the S-transform are widely used signal processing tools for extracting frequency information from non-stationary signals. Previously, the windowed Fourier transform had been adopted for signals on graphs and has been shown to be very useful for extracting vertex-frequency information from graphs. However, high computational complexity makes these algorithms impractical. We sought to develop a fast windowed graph Fourier transform and a fast graph S-transform requiring significantly shorter computation time. The proposed schemes have been tested with synthetic test graph signals and real graph signals derived from electroencephalography recordings made during swallowing. The results showed that the proposed schemes provide significantly lower computation time in comparison with the standard windowed graph Fourier transform and the fast graph S-transform. Also, the results showed that noise has no effect on the results of the algorithm for the fast windowed graph Fourier transform or on the graph S-transform. Finally, we showed that graphs can be reconstructed from the vertex-frequency representations obtained with the proposed algorithms. PMID:28479645

Matrix form for the instrument line shape of Fourier-transform spectrometers yielding a fast integration algorithm to theoretical spectra.

PubMed

Desbiens, Raphaël; Tremblay, Pierre; Genest, Jérôme; Bouchard, Jean-Pierre

2006-01-20

The instrument line shape (ILS) of a Fourier-transform spectrometer is expressed in a matrix form. For all line shape effects that scale with wavenumber, the ILS matrix is shown to be transposed in the spectral and interferogram domains. The novel representation of the ILS matrix in the interferogram domain yields an insightful physical interpretation of the underlying process producing self-apodization. Working in the interferogram domain circumvents the problem of taking into account the effects of finite optical path difference and permits a proper discretization of the equations. A fast algorithm in O(N log2 N), based on the fractional Fourier transform, is introduced that permits the application of a constant resolving power line shape to theoretical spectra or forward models. The ILS integration formalism is validated with experimental data.

Angle-resolved light scattering of individual rod-shaped bacteria based on Fourier transform light scattering

NASA Astrophysics Data System (ADS)

Jo, Youngju; Jung, Jaehwang; Lee, Jee Woong; Shin, Della; Park, Hyunjoo; Nam, Ki Tae; Park, Ji-Ho; Park, Yongkeun

2014-05-01

Two-dimensional angle-resolved light scattering maps of individual rod-shaped bacteria are measured at the single-cell level. Using quantitative phase imaging and Fourier transform light scattering techniques, the light scattering patterns of individual bacteria in four rod-shaped species (Bacillus subtilis, Lactobacillus casei, Synechococcus elongatus, and Escherichia coli) are measured with unprecedented sensitivity in a broad angular range from -70° to 70°. The measured light scattering patterns are analyzed along the two principal axes of rod-shaped bacteria in order to systematically investigate the species-specific characteristics of anisotropic light scattering. In addition, the cellular dry mass of individual bacteria is calculated and used to demonstrate that the cell-to-cell variations in light scattering within bacterial species is related to the cellular dry mass and growth.

Fourier transform spectrometer observations of solar carbon monoxide. III - Time-resolved spectroscopy of the Delta V = 1 bands

NASA Astrophysics Data System (ADS)

Ayres, Thomas R.; Brault, James W.

1990-11-01

Time series of the 2100/cm Delta v = 1 absorption bands of CO at the center of the solar disk and at the extreme limb have been recorded by Fourier transform spectrometer. The photospheric 5-min oscillation appears prominently at sun center. The peak-to-peak brightness temperature amplitude is roughly 300 K, and the peak-to-peak Doppler shift is roughly 1100 m/s. The 70 deg phase lag of maximum core intensity with respect to maximum redshift for the strongest Delta v = 1 absorptions is less than the 90 deg expected in the adiabatic limit. No dominant four-minute signal in the line intensity like that reported by Deming et al. (1984, 1986, and 1987) is found, nor is evidence for extreme fluctuations on short time scales like those proposed by Kalkofen et al. (1984). The strong Delta v = 1 lines exhibit systematic Doppler shifts of less than about 1 km/s, contrary to the predictions of transonic redshifts if the CO 'clouds' are associated with a dynamic cooling phase of the Ca II 'cell flashes.'

Far-field radiation patterns of aperture antennas by the Winograd Fourier transform algorithm

NASA Technical Reports Server (NTRS)

Heisler, R.

1978-01-01

A more time-efficient algorithm for computing the discrete Fourier transform, the Winograd Fourier transform (WFT), is described. The WFT algorithm is compared with other transform algorithms. Results indicate that the WFT algorithm in antenna analysis appears to be a very successful application. Significant savings in cpu time will improve the computer turn around time and circumvent the need to resort to weekend runs.

Light diffusion in N-layered turbid media: steady-state domain.

PubMed

Liemert, André; Kienle, Alwin

2010-01-01

We deal with light diffusion in N-layered turbid media. The steady-state diffusion equation is solved for N-layered turbid media having a finite or an infinitely thick N'th layer. Different refractive indices are considered in the layers. The Fourier transform formalism is applied to derive analytical solutions of the fluence rate in Fourier space. The inverse Fourier transform is calculated using four different methods to test their performance and accuracy. Further, to avoid numerical errors, approximate formulas in Fourier space are derived. Fast solutions for calculation of the spatially resolved reflectance and transmittance from the N-layered turbid media ( approximately 10 ms) with small relative differences (<10(-7)) are found. Additionally, the solutions of the diffusion equation are compared to Monte Carlo simulations for turbid media having up to 20 layers.

Electro-Optical Imaging Fourier-Transform Spectrometer

NASA Technical Reports Server (NTRS)

Chao, Tien-Hsin; Zhou, Hanying

2006-01-01

An electro-optical (E-O) imaging Fourier-transform spectrometer (IFTS), now under development, is a prototype of improved imaging spectrometers to be used for hyperspectral imaging, especially in the infrared spectral region. Unlike both imaging and non-imaging traditional Fourier-transform spectrometers, the E-O IFTS does not contain any moving parts. Elimination of the moving parts and the associated actuator mechanisms and supporting structures would increase reliability while enabling reductions in size and mass, relative to traditional Fourier-transform spectrometers that offer equivalent capabilities. Elimination of moving parts would also eliminate the vibrations caused by the motions of those parts. Figure 1 schematically depicts a traditional Fourier-transform spectrometer, wherein a critical time delay is varied by translating one the mirrors of a Michelson interferometer. The time-dependent optical output is a periodic representation of the input spectrum. Data characterizing the input spectrum are generated through fast-Fourier-transform (FFT) post-processing of the output in conjunction with the varying time delay.

Differences between time domain and Fourier domain optical coherence tomography in imaging tissues.

PubMed

Gao, W; Wu, X

2017-11-01

It has been numerously demonstrated that both time domain and Fourier domain optical coherence tomography (OCT) can generate high-resolution depth-resolved images of living tissues and cells. In this work, we compare the common points and differences between two methods when the continuous and random properties of live tissue are taken into account. It is found that when relationships that exist between the scattered light and tissue structures are taken into account, spectral interference measurements in Fourier domain OCT (FDOCT) is more advantageous than interference fringe envelope measurements in time domain OCT (TDOCT) in the cases where continuous property of tissue is taken into account. It is also demonstrated that when random property of tissue is taken into account FDOCT measures the Fourier transform of the spatial correlation function of the refractive index and speckle phenomena will limit the effective limiting imaging resolution in both TDOCT and FDOCT. Finally, the effective limiting resolution of both TDOCT and FDOCT are given which can be used to estimate the effective limiting resolution in various practical applications. © 2017 The Authors Journal of Microscopy © 2017 Royal Microscopical Society.

Precise and fast spatial-frequency analysis using the iterative local Fourier transform.

PubMed

Lee, Sukmock; Choi, Heejoo; Kim, Dae Wook

2016-09-19

The use of the discrete Fourier transform has decreased since the introduction of the fast Fourier transform (fFT), which is a numerically efficient computing process. This paper presents the iterative local Fourier transform (ilFT), a set of new processing algorithms that iteratively apply the discrete Fourier transform within a local and optimal frequency domain. The new technique achieves 2¹⁰ times higher frequency resolution than the fFT within a comparable computation time. The method's superb computing efficiency, high resolution, spectrum zoom-in capability, and overall performance are evaluated and compared to other advanced high-resolution Fourier transform techniques, such as the fFT combined with several fitting methods. The effectiveness of the ilFT is demonstrated through the data analysis of a set of Talbot self-images (1280 × 1024 pixels) obtained with an experimental setup using grating in a diverging beam produced by a coherent point source.

Big data in reciprocal space: Sliding fast Fourier transforms for determining periodicity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Vasudevan, Rama K., E-mail: rvv@ornl.gov; Belianinov, Alex; Baddorf, Arthur P.

Significant advances in atomically resolved imaging of crystals and surfaces have occurred in the last decade allowing unprecedented insight into local crystal structures and periodicity. Yet, the analysis of the long-range periodicity from the local imaging data, critical to correlation of functional properties and chemistry to the local crystallography, remains a challenge. Here, we introduce a Sliding Fast Fourier Transform (FFT) filter to analyze atomically resolved images of in-situ grown La{sub 5/8}Ca{sub 3/8}MnO{sub 3} (LCMO) films. We demonstrate the ability of sliding FFT algorithm to differentiate two sub-lattices, resulting from a mixed-terminated surface. Principal Component Analysis and Independent Component Analysismore » of the Sliding FFT dataset reveal the distinct changes in crystallography, step edges, and boundaries between the multiple sub-lattices. The implications for the LCMO system are discussed. The method is universal for images with any periodicity, and is especially amenable to atomically resolved probe and electron-microscopy data for rapid identification of the sub-lattices present.« less

Surface-Induced Dissociation of Protein Complexes in a Hybrid Fourier Transform Ion Cyclotron Resonance Mass Spectrometer.

PubMed

Yan, Jing; Zhou, Mowei; Gilbert, Joshua D; Wolff, Jeremy J; Somogyi, Árpád; Pedder, Randall E; Quintyn, Royston S; Morrison, Lindsay J; Easterling, Michael L; Paša-Tolić, Ljiljana; Wysocki, Vicki H

2017-01-03

Mass spectrometry continues to develop as a valuable tool in the analysis of proteins and protein complexes. In protein complex mass spectrometry studies, surface-induced dissociation (SID) has been successfully applied in quadrupole time-of-flight (Q-TOF) instruments. SID provides structural information on noncovalent protein complexes that is complementary to other techniques. However, the mass resolution of Q-TOF instruments can limit the information that can be obtained for protein complexes by SID. Fourier transform ion cyclotron resonance mass spectrometry (FT-ICR MS) provides ultrahigh resolution and ultrahigh mass accuracy measurements. In this study, an SID device was designed and successfully installed in a hybrid FT-ICR instrument in place of the standard gas collision cell. The SID-FT-ICR platform has been tested with several protein complex systems (homooligomers, a heterooligomer, and a protein-ligand complex, ranging from 53 to 85 kDa), and the results are consistent with data previously acquired on Q-TOF platforms, matching predictions from known protein interface information. SID fragments with the same m/z but different charge states are well-resolved based on distinct spacing between adjacent isotope peaks, and the addition of metal cations and ligands can also be isotopically resolved with the ultrahigh mass resolution available in FT-ICR.

Driving force behind adsorption-induced protein unfolding: a time-resolved X-ray reflectivity study on lysozyme adsorbed at an air/water interface.

PubMed

Yano, Yohko F; Uruga, Tomoya; Tanida, Hajime; Toyokawa, Hidenori; Terada, Yasuko; Takagaki, Masafumi; Yamada, Hironari

2009-01-06

Time-resolved X-ray reflectivity measurements for lysozyme (LSZ) adsorbed at an air/water interface were performed to study the mechanism of adsorption-induced protein unfolding. The time dependence of the density profile at the air/water interface revealed that the molecular conformation changed significantly during adsorption. Taking into account previous work using Fourier transform infrared (FTIR) spectroscopy, we propose that the LSZ molecules initially adsorbed on the air/water interface have a flat unfolded structure, forming antiparallel beta-sheets as a result of hydrophobic interactions with the gas phase. In contrast, as adsorption continues, a second layer forms in which the molecules have a very loose structure having random coils as a result of hydrophilic interactions with the hydrophilic groups that protrude from the first layer.

Properties of the Magnitude Terms of Orthogonal Scaling Functions.

PubMed

Tay, Peter C; Havlicek, Joseph P; Acton, Scott T; Hossack, John A

2010-09-01

The spectrum of the convolution of two continuous functions can be determined as the continuous Fourier transform of the cross-correlation function. The same can be said about the spectrum of the convolution of two infinite discrete sequences, which can be determined as the discrete time Fourier transform of the cross-correlation function of the two sequences. In current digital signal processing, the spectrum of the contiuous Fourier transform and the discrete time Fourier transform are approximately determined by numerical integration or by densely taking the discrete Fourier transform. It has been shown that all three transforms share many analogous properties. In this paper we will show another useful property of determining the spectrum terms of the convolution of two finite length sequences by determining the discrete Fourier transform of the modified cross-correlation function. In addition, two properties of the magnitude terms of orthogonal wavelet scaling functions are developed. These properties are used as constraints for an exhaustive search to determine an robust lower bound on conjoint localization of orthogonal scaling functions.

Double Fourier analysis for Emotion Identification in Voiced Speech

NASA Astrophysics Data System (ADS)

Sierra-Sosa, D.; Bastidas, M.; Ortiz P., D.; Quintero, O. L.

2016-04-01

We propose a novel analysis alternative, based on two Fourier Transforms for emotion recognition from speech. Fourier analysis allows for display and synthesizes different signals, in terms of power spectral density distributions. A spectrogram of the voice signal is obtained performing a short time Fourier Transform with Gaussian windows, this spectrogram portraits frequency related features, such as vocal tract resonances and quasi-periodic excitations during voiced sounds. Emotions induce such characteristics in speech, which become apparent in spectrogram time-frequency distributions. Later, the signal time-frequency representation from spectrogram is considered an image, and processed through a 2-dimensional Fourier Transform in order to perform the spatial Fourier analysis from it. Finally features related with emotions in voiced speech are extracted and presented.

A method of power analysis based on piecewise discrete Fourier transform

NASA Astrophysics Data System (ADS)

Xin, Miaomiao; Zhang, Yanchi; Xie, Da

2018-04-01

The paper analyzes the existing feature extraction methods. The characteristics of discrete Fourier transform and piecewise aggregation approximation are analyzed. Combining with the advantages of the two methods, a new piecewise discrete Fourier transform is proposed. And the method is used to analyze the lighting power of a large customer in this paper. The time series feature maps of four different cases are compared with the original data, discrete Fourier transform, piecewise aggregation approximation and piecewise discrete Fourier transform. This new method can reflect both the overall trend of electricity change and its internal changes in electrical analysis.

Fourier transform infrared difference and time-resolved infrared detection of the electron and proton transfer dynamics in photosynthetic water oxidation.

PubMed

Noguchi, Takumi

2015-01-01

Photosynthetic water oxidation, which provides the electrons necessary for CO₂ reduction and releases O₂ and protons, is performed at the Mn₄CaO₅ cluster in photosystem II (PSII). In this review, studies that assessed the mechanism of water oxidation using infrared spectroscopy are summarized focusing on electron and proton transfer dynamics. Structural changes in proteins and water molecules between intermediates known as Si states (i=0-3) were detected using flash-induced Fourier transform infrared (FTIR) difference spectroscopy. Electron flow in PSII and proton release from substrate water were monitored using the infrared changes in ferricyanide as an exogenous electron acceptor and Mes buffer as a proton acceptor. Time-resolved infrared (TRIR) spectroscopy provided information on the dynamics of proton-coupled electron transfer during the S-state transitions. In particular, a drastic proton movement during the lag phase (~200μs) before electron transfer in the S3→S0 transition was detected directly by monitoring the infrared absorption of a polarizable proton in a hydrogen bond network. Furthermore, the proton release pathways in the PSII proteins were analyzed by FTIR difference measurements in combination with site-directed mutagenesis, isotopic substitutions, and quantum chemical calculations. Therefore, infrared spectroscopy is a powerful tool for understanding the molecular mechanism of photosynthetic water oxidation. This article is part of a Special Issue entitled: Vibrational spectroscopies and bioenergetic systems. Copyright © 2014 Elsevier B.V. All rights reserved.

Next generation techniques in the high resolution spectroscopy of biologically relevant molecules.

PubMed

Neill, Justin L; Douglass, Kevin O; Pate, Brooks H; Pratt, David W

2011-04-28

Recent advances in the technology of test and measurement equipment driven by the computer and telecommunications industries have made possible the development of a new broadband, Fourier-transform microwave spectrometer that operates on principles similar to FTNMR. This technique uses a high sample-rate arbitrary waveform generator to construct a phase-locked chirped microwave pulse that gives a linear frequency sweep over a wide frequency range in 1 μs. The chirped pulse efficiently polarizes the molecular sample at all frequencies lying within this band. The subsequent free induction decay of this polarization is measured with a high-speed digitizer and then fast Fourier-transformed to yield a broadband, frequency-resolved rotational spectrum, spanning up to 11.5 GHz and containing lines that are as narrow as 100 kHz. This new technique is called chirped-pulse Fourier transform microwave (CP-FTMW) spectroscopy. The technique offers the potential to determine the structural and dynamical properties of very large molecules solely from fully resolved pure rotational spectra. FTMW double resonance techniques employing a low-resolution UV laser facilitate an easy assignment of overlapping spectra produced by different conformers in the sample. Of particular interest are the energy landscapes of conformationally flexible molecules of biological importance, including studies of their interaction with solvent and/or other weakly bound molecules. An example is provided from the authors' work on p-methoxyphenethylamine, a neurotransmitter, and its complexes with water.

A new hybrid electrospray Fourier transform mass spectrometer: design and performance characteristics.

PubMed

O'connor, Peter B; Pittman, Jason L; Thomson, Bruce A; Budnik, Bogdan A; Cournoyer, Jason C; Jebanathirajah, Judith; Lin, Cheng; Moyer, Susanne; Zhao, Cheng

2006-01-01

A new hybrid electrospray quadrupole Fourier transform mass spectrometry (FTMS) instrument design is shown and characterized. This instrument involves coupling an electrospray source and mass-resolving quadrupole, ion accumulation, and collision cell linear ion trap system developed by MDS Sciex with a home-built ion guide and ion cyclotron resonance (ICR) cell. The iterative progression of this design is shown. The final design involves a set of hexapole ion guides to transfer the ions from the accumulation/collision trap through the magnetic field gradient and into the cell. These hexapole ion guides are separated by a thin gate valve and two conduction limits to maintain the required <10(-9) mbar vacuum for FTICR. Low-attomole detection limits for a pure peptide are shown, 220 000 resolving power in broadband mode and 820 000 resolving power in narrow-band mode are demonstrated, and mass accuracy in the <2 ppm range is routinely available provided the signal is abundant, cleanly resolved, and internally calibrated. This instrument design provides high experimental flexibility, allowing Q2 CAD, SORI-CAD, IRMPD, and ECD experiments with selected ion accumulation as well as experiments such as nozzle skimmer dissociation. Initial top-down mass spectrometry experiments on a protein is shown using ECD.

Rapid update of discrete Fourier transform for real-time signal processing

NASA Astrophysics Data System (ADS)

Sherlock, Barry G.; Kakad, Yogendra P.

2001-10-01

In many identification and target recognition applications, the incoming signal will have properties that render it amenable to analysis or processing in the Fourier domain. In such applications, however, it is usually essential that the identification or target recognition be performed in real time. An important constraint upon real-time processing in the Fourier domain is the time taken to perform the Discrete Fourier Transform (DFT). Ideally, a new Fourier transform should be obtained after the arrival of every new data point. However, the Fast Fourier Transform (FFT) algorithm requires on the order of N log2 N operations, where N is the length of the transform, and this usually makes calculation of the transform for every new data point computationally prohibitive. In this paper, we develop an algorithm to update the existing DFT to represent the new data series that results when a new signal point is received. Updating the DFT in this way uses less computational order by a factor of log2 N. The algorithm can be modified to work in the presence of data window functions. This is a considerable advantage, because windowing is often necessary to reduce edge effects that occur because the implicit periodicity of the Fourier transform is not exhibited by the real-world signal. Versions are developed in this paper for use with the boxcar window, the split triangular, Hanning, Hamming, and Blackman windows. Generalization of these results to 2D is also presented.

Practical Sub-Nyquist Sampling via Array-Based Compressed Sensing Receiver Architecture

DTIC Science & Technology

2016-07-10

different array ele- ments at different sub-Nyquist sampling rates. Signal processing inspired by the sparse fast Fourier transform allows for signal...reconstruction algorithms can be computationally demanding (REF). The related sparse Fourier transform algorithms aim to reduce the processing time nec- essary to...compute the DFT of frequency-sparse signals [7]. In particular, the sparse fast Fourier transform (sFFT) achieves processing time better than the

An Introduction to Fast Fourier Transforms through the Study of Oscillating Reactions.

ERIC Educational Resources Information Center

Eastman, M. P.; And Others

1986-01-01

Discusses an experiment designed to introduce students to the basic principles of the fast Fourier transform and Fourier smoothing through transformation of time-dependent optical absorption data from an oscillating reaction. Uses the Belousov-Zhabotinskii reaction. Describes the experimental setup and data analysis techniques.

Modified slanted-edge method for camera modulation transfer function measurement using nonuniform fast Fourier transform technique

NASA Astrophysics Data System (ADS)

Duan, Yaxuan; Xu, Songbo; Yuan, Suochao; Chen, Yongquan; Li, Hongguang; Da, Zhengshang; Gao, Limin

2018-01-01

ISO 12233 slanted-edge method experiences errors using fast Fourier transform (FFT) in the camera modulation transfer function (MTF) measurement due to tilt angle errors in the knife-edge resulting in nonuniform sampling of the edge spread function (ESF). In order to resolve this problem, a modified slanted-edge method using nonuniform fast Fourier transform (NUFFT) for camera MTF measurement is proposed. Theoretical simulations for images with noise at a different nonuniform sampling rate of ESF are performed using the proposed modified slanted-edge method. It is shown that the proposed method successfully eliminates the error due to the nonuniform sampling of the ESF. An experimental setup for camera MTF measurement is established to verify the accuracy of the proposed method. The experiment results show that under different nonuniform sampling rates of ESF, the proposed modified slanted-edge method has improved accuracy for the camera MTF measurement compared to the ISO 12233 slanted-edge method.

A boostrap algorithm for temporal signal reconstruction in the presence of noise from its fractional Fourier transformed intensity spectra

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tan, Cheng-Yang; /Fermilab

2011-02-01

A bootstrap algorithm for reconstructing the temporal signal from four of its fractional Fourier intensity spectra in the presence of noise is described. An optical arrangement is proposed which realises the bootstrap method for the measurement of ultrashort laser pulses. The measurement of short laser pulses which are less than 1 ps is an ongoing challenge in optical physics. One reason is that no oscilloscope exists today which can directly measure the time structure of these pulses and so it becomes necessary to invent other techniques which indirectly provide the necessary information for temporal pulse reconstruction. One method called FROGmore » (frequency resolved optical gating) has been in use since 19911 and is one of the popular methods for recovering these types of short pulses. The idea behind FROG is the use of multiple time-correlated pulse measurements in the frequency domain for the reconstruction. Multiple data sets are required because only intensity information is recorded and not phase, and thus by collecting multiple data sets, there is enough redundant measurements to yield the original time structure, but not necessarily uniquely (or even up to an arbitrary constant phase offset). The objective of this paper is to describe another method which is simpler than FROG. Instead of collecting many auto-correlated data sets, only two spectral intensity measurements of the temporal signal are needed in the absence of noise. The first can be from the intensity components of its usual Fourier transform and the second from its FrFT (fractional Fourier transform). In the presence of noise, a minimum of four measurements are required with the same FrFT order but with two different apertures. Armed with these two or four measurements, a unique solution up to a constant phase offset can be constructed.« less

Study on the conformation changes of Lysozyme induced by Hypocrellin A: The mechanism investigation

NASA Astrophysics Data System (ADS)

Ma, Fei; Huang, He-Yong; Zhou, Lin; Yang, Chao; Zhou, Jia-Hong; Liu, Zheng-Ming

2012-11-01

The interactions between Lysozyme and Hypocrellin A are investigated in details using time-resolved fluorescence, fourier transform infrared spectroscopy (FTIR), circular dichroism spectroscopy (CD), three-dimensional fluorescence spectra, and thermal gravimetric analysis (TGA) techniques. The results of time-resolved fluorescence suggest that the quenching mechanism is static quenching. FTIR and CD spectroscopy provide evidences of the reducing of α-helix after interaction. Hypocrellin A could change the micro-environmental of Lysozyme according to hydrophobic interaction between the aromatic ring and the hydrophobic amino acid residues, and the altered polypeptide backbone structures induce the reduction of α-helical structures. Moreover, TGA study further demonstrates the structure changes of Lysozyme on the effect of Hypocrellin A. This study could provide some important information for the derivatives of HA in pharmacy, pharmacology and biochemistry.

Gas Chromatography/Atmospheric Pressure Chemical Ionization-Fourier Transform Ion Cyclotron Resonance Mass Spectrometry of Pyrolysis Oil from German Brown Coal

PubMed Central

Zuber, Jan; Kroll, Marius M.; Rathsack, Philipp; Otto, Matthias

2016-01-01

Pyrolysis oil from the slow pyrolysis of German brown coal from Schöningen, obtained at a temperature of 500°C, was separated and analyzed using hyphenation of gas chromatography with an atmospheric pressure chemical ionization source operated in negative ion mode and Fourier transform ion cyclotron resonance mass spectrometry (GC-APCI-FT-ICR-MS). Development of this ultrahigh-resolving analysis method is described, that is, optimization of specific GC and APCI parameters and performed data processing. The advantages of GC-APCI-FT-ICR-MS hyphenation, for example, soft ionization, ultrahigh-resolving detection, and most important isomer separation, were demonstrated for the sample liquid. For instance, it was possible to separate and identify nine different propylphenol, ethylmethylphenol, and trimethylphenol isomers. Furthermore, homologous series of different acids, for example, alkyl and alkylene carboxylic acids, were verified, as well as homologous series of alkyl phenols, alkyl dihydroxy benzenes, and alkoxy alkyl phenols. PMID:27066076

Surface-Induced Dissociation of Protein Complexes in a Hybrid Fourier Transform Ion Cyclotron Resonance Mass Spectrometer

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yan, Jing; Zhou, Mowei; Gilbert, Joshua D.

Mass spectrometry continues to develop as a valuable tool in the analysis of proteins and protein complexes. In protein complex mass spectrometry studies, surface-induced dissociation (SID) has been successfully applied in quadrupole time-of-flight (Q-TOF) instruments. SID provides structural information on noncovalent protein complexes that is complementary to other techniques. However, the mass resolution of Q-TOF instruments can limit the information that can be obtained for protein complexes by SID. Fourier transform ion cyclotron resonance mass spectrometry (FT-ICR MS) provides ultrahigh resolution and ultrahigh mass accuracy measurements. Here in this study, an SID device was designed and successfully installed in amore » hybrid FT-ICR instrument in place of the standard gas collision cell. The SID-FT-ICR platform has been tested with several protein complex systems (homooligomers, a heterooligomer, and a protein-ligand complex, ranging from 53 to 85 kDa), and the results are consistent with data previously acquired on Q-TOF platforms, matching predictions from known protein interface information. Lastly, SID fragments with the same m/z but different charge states are well-resolved based on distinct spacing between adjacent isotope peaks, and the addition of metal cations and ligands can also be isotopically resolved with the ultrahigh mass resolution available in FT-ICR.« less

Surface-Induced Dissociation of Protein Complexes in a Hybrid Fourier Transform Ion Cyclotron Resonance Mass Spectrometer

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yan, Jing; Zhou, Mowei; Gilbert, Joshua D.

Mass spectrometry continues to develop as a valuable tool in the analysis of proteins and protein complexes. In protein complex mass spectrometry studies, surface-induced dissociation (SID) has been successfully applied in quadrupole time-of-flight (Q-TOF) instruments. SID provides structural information on non-covalent protein complexes that is complementary to other techniques. However, the mass resolution of Q-TOF instruments can limit the information that can be obtained for protein complexes by SID. Fourier transform ion cyclotron resonance mass spectrometry (FT-ICR MS) provides ultrahigh resolution and ultrahigh mass accuracy measurements. In this study, an SID device was designed and successfully installed in a hybridmore » FT-ICR instrument in place of the standard gas collision cell. The SID-FT-ICR platform has been tested with several protein complex systems (homooligomers, a heterooligomer, and a protein-ligand complex, ranging from 53 kDa to 85 kDa), and the results are consistent with data previously acquired on Q-TOF platforms, matching predictions from known protein interface information. SID fragments with the same m/z but different charge states are well-resolved based on distinct spacing between adjacent isotope peaks, and the addition of metal cations and ligands can also be isotopically resolved with the ultrahigh mass resolution available in FT-ICR.« less

Surface-Induced Dissociation of Protein Complexes in a Hybrid Fourier Transform Ion Cyclotron Resonance Mass Spectrometer

DOE PAGES

Yan, Jing; Zhou, Mowei; Gilbert, Joshua D.; ...

2016-12-02

Mass spectrometry continues to develop as a valuable tool in the analysis of proteins and protein complexes. In protein complex mass spectrometry studies, surface-induced dissociation (SID) has been successfully applied in quadrupole time-of-flight (Q-TOF) instruments. SID provides structural information on noncovalent protein complexes that is complementary to other techniques. However, the mass resolution of Q-TOF instruments can limit the information that can be obtained for protein complexes by SID. Fourier transform ion cyclotron resonance mass spectrometry (FT-ICR MS) provides ultrahigh resolution and ultrahigh mass accuracy measurements. Here in this study, an SID device was designed and successfully installed in amore » hybrid FT-ICR instrument in place of the standard gas collision cell. The SID-FT-ICR platform has been tested with several protein complex systems (homooligomers, a heterooligomer, and a protein-ligand complex, ranging from 53 to 85 kDa), and the results are consistent with data previously acquired on Q-TOF platforms, matching predictions from known protein interface information. Lastly, SID fragments with the same m/z but different charge states are well-resolved based on distinct spacing between adjacent isotope peaks, and the addition of metal cations and ligands can also be isotopically resolved with the ultrahigh mass resolution available in FT-ICR.« less

Real-time processing for full-range Fourier-domain optical-coherence tomography with zero-filling interpolation using multiple graphic processing units.

PubMed

Watanabe, Yuuki; Maeno, Seiya; Aoshima, Kenji; Hasegawa, Haruyuki; Koseki, Hitoshi

2010-09-01

The real-time display of full-range, 2048?axial pixelx1024?lateral pixel, Fourier-domain optical-coherence tomography (FD-OCT) images is demonstrated. The required speed was achieved by using dual graphic processing units (GPUs) with many stream processors to realize highly parallel processing. We used a zero-filling technique, including a forward Fourier transform, a zero padding to increase the axial data-array size to 8192, an inverse-Fourier transform back to the spectral domain, a linear interpolation from wavelength to wavenumber, a lateral Hilbert transform to obtain the complex spectrum, a Fourier transform to obtain the axial profiles, and a log scaling. The data-transfer time of the frame grabber was 15.73?ms, and the processing time, which includes the data transfer between the GPU memory and the host computer, was 14.75?ms, for a total time shorter than the 36.70?ms frame-interval time using a line-scan CCD camera operated at 27.9?kHz. That is, our OCT system achieved a processed-image display rate of 27.23 frames/s.

Non-stationary component extraction in noisy multicomponent signal using polynomial chirping Fourier transform.

PubMed

Lu, Wenlong; Xie, Junwei; Wang, Heming; Sheng, Chuan

2016-01-01

Inspired by track-before-detection technology in radar, a novel time-frequency transform, namely polynomial chirping Fourier transform (PCFT), is exploited to extract components from noisy multicomponent signal. The PCFT combines advantages of Fourier transform and polynomial chirplet transform to accumulate component energy along a polynomial chirping curve in the time-frequency plane. The particle swarm optimization algorithm is employed to search optimal polynomial parameters with which the PCFT will achieve a most concentrated energy ridge in the time-frequency plane for the target component. The component can be well separated in the polynomial chirping Fourier domain with a narrow-band filter and then reconstructed by inverse PCFT. Furthermore, an iterative procedure, involving parameter estimation, PCFT, filtering and recovery, is introduced to extract components from a noisy multicomponent signal successively. The Simulations and experiments show that the proposed method has better performance in component extraction from noisy multicomponent signal as well as provides more time-frequency details about the analyzed signal than conventional methods.

Resolvent estimates in homogenisation of periodic problems of fractional elasticity

NASA Astrophysics Data System (ADS)

Cherednichenko, Kirill; Waurick, Marcus

2018-03-01

We provide operator-norm convergence estimates for solutions to a time-dependent equation of fractional elasticity in one spatial dimension, with rapidly oscillating coefficients that represent the material properties of a viscoelastic composite medium. Assuming periodicity in the coefficients, we prove operator-norm convergence estimates for an operator fibre decomposition obtained by applying to the original fractional elasticity problem the Fourier-Laplace transform in time and Gelfand transform in space. We obtain estimates on each fibre that are uniform in the quasimomentum of the decomposition and in the period of oscillations of the coefficients as well as quadratic with respect to the spectral variable. On the basis of these uniform estimates we derive operator-norm-type convergence estimates for the original fractional elasticity problem, for a class of sufficiently smooth densities of applied forces.

Causal Correlation Functions and Fourier Transforms: Application in Calculating Pressure Induced Shifts

NASA Technical Reports Server (NTRS)

Ma, Q.; Tipping, R. H.; Lavrentieva, N. N.

2012-01-01

By adopting a concept from signal processing, instead of starting from the correlation functions which are even, one considers the causal correlation functions whose Fourier transforms become complex. Their real and imaginary parts multiplied by 2 are the Fourier transforms of the original correlations and the subsequent Hilbert transforms, respectively. Thus, by taking this step one can complete the two previously needed transforms. However, to obviate performing the Cauchy principal integrations required in the Hilbert transforms is the greatest advantage. Meanwhile, because the causal correlations are well-bounded within the time domain and band limited in the frequency domain, one can replace their Fourier transforms by the discrete Fourier transforms and the latter can be carried out with the FFT algorithm. This replacement is justified by sampling theory because the Fourier transforms can be derived from the discrete Fourier transforms with the Nyquis rate without any distortions. We apply this method in calculating pressure induced shifts of H2O lines and obtain more reliable values. By comparing the calculated shifts with those in HITRAN 2008 and by screening both of them with the pair identity and the smooth variation rules, one can conclude many of shift values in HITRAN are not correct.

Time-resolved spectral characterization of ring cavity surface emitting and ridge-type distributed feedback quantum cascade lasers by step-scan FT-IR spectroscopy.

PubMed

Brandstetter, Markus; Genner, Andreas; Schwarzer, Clemens; Mujagic, Elvis; Strasser, Gottfried; Lendl, Bernhard

2014-02-10

We present the time-resolved comparison of pulsed 2nd order ring cavity surface emitting (RCSE) quantum cascade lasers (QCLs) and pulsed 1st order ridge-type distributed feedback (DFB) QCLs using a step-scan Fourier transform infrared (FT-IR) spectrometer. Laser devices were part of QCL arrays and fabricated from the same laser material. Required grating periods were adjusted to account for the grating order. The step-scan technique provided a spectral resolution of 0.1 cm(-1) and a time resolution of 2 ns. As a result, it was possible to gain information about the tuning behavior and potential mode-hops of the investigated lasers. Different cavity-lengths were compared, including 0.9 mm and 3.2 mm long ridge-type and 0.97 mm (circumference) ring-type cavities. RCSE QCLs were found to have improved emission properties in terms of line-stability, tuning rate and maximum emission time compared to ridge-type lasers.

Ultra-Wideband Radar Transient Detection using Time-Frequency and Wavelet Transforms.

DTIC Science & Technology

1992-12-01

if p==2, mesh(flipud(abs(spdatamatrix).A2)) end 2. Wigner - Ville Distribution function P = wvd (data,winlenstep,begintheendp) % Filename: wvd.m % Title...short time Fourier transform (STFT), the Instantaneous Power Spectrum and the Wigner - Ville distribution , and time-scale methods, such as the a trous...such as the short time Fourier transform (STFT), the Instantaneous Power Spectrum and the Wigner - Ville distribution [1], and time-scale methods, such

Bessel function expansion to reduce the calculation time and memory usage for cylindrical computer-generated holograms.

PubMed

Sando, Yusuke; Barada, Daisuke; Jackin, Boaz Jessie; Yatagai, Toyohiko

2017-07-10

This study proposes a method to reduce the calculation time and memory usage required for calculating cylindrical computer-generated holograms. The wavefront on the cylindrical observation surface is represented as a convolution integral in the 3D Fourier domain. The Fourier transformation of the kernel function involving this convolution integral is analytically performed using a Bessel function expansion. The analytical solution can drastically reduce the calculation time and the memory usage without any cost, compared with the numerical method using fast Fourier transform to Fourier transform the kernel function. In this study, we present the analytical derivation, the efficient calculation of Bessel function series, and a numerical simulation. Furthermore, we demonstrate the effectiveness of the analytical solution through comparisons of calculation time and memory usage.

A Short-Segment Fourier Transform Methodology

DTIC Science & Technology

2009-03-01

defined sampling of the continuous-valued discrete-time Fourier transform, superresolution in the frequency domain and allowance of Dirac delta functions associated with pure sinusoidal input data components.

Observation of Pure Rotational Spectra of SiCCN by Fourier-Transform Microwave Spectroscopy

NASA Astrophysics Data System (ADS)

Umeki, Hiroya; Nakajima, Masakazu; Endo, Yasuki

2014-06-01

Pure rotational spectra of SiCCN ( ˜{X} 2Π3/2) have been observed using Fourier-transform microwave (FTMW) spectroscopy in the frequency region 13 to 35 GHz. The SiCCN radical was produced in a supersonic jet by discharging a mixture gas, 0.2% SiCl4 and 0.2% CH3CN diluted in Ar. The effective rotational constant Beff,3/2, the centrifugal distortion constant D, and the hyperfine coupling constants, a + (b + c)/2 and eQq0, were determined with a standard deviation of the fit to be 6 kHz. Determined B and eQq0 are consistent with those derived from ab initio calculations. Λ-type doublings were not resolved for the observed spectra.

Improved ion optics for introduction of ions into a 9.4-T Fourier transform ion cyclotron resonance mass spectrometer

DOE PAGES

Chen, Yu; Leach, Franklin E.; Kaiser, Nathan K.; ...

2015-01-19

Fourier transform ion cyclotron resonance (FT-ICR) mass spectrometry provides unparalleled mass accuracy and resolving power.[1],[2] With electrospray ionization (ESI), ions are typically transferred into the mass spectrometer through a skimmer, which serves as a conductance-limiting orifice. However, the skimmer allows only a small fraction of incoming ions to enter the mass spectrometer. An ion funnel, originally developed by Smith and coworkers at Pacific Northwest National Laboratory (PNNL)[3-5] provides much more efficient ion focusing and transfer. The large entrance aperture of the ion funnel allows almost all ions emanating from a heated capillary to be efficiently captured and transferred, resulting inmore » nearly lossless transmission.« less

Concerning the Spatial Heterodyne Spectrometer

DOE PAGES

Lenzner, Matthias; Diels, Jean -Claude

2016-01-22

A modified Spatial Heterodyne Spectrometer (SHS) is used for measuring atomic emission spectra with high resolution. This device is basically a Fourier Transform Spectrometer, but the Fourier transform is taken in the directions perpendicular to the optical propagation and heterodyned around one preset wavelength. In recent descriptions of this device, one specific phenomenon - the tilt of the energy front of wave packets when diffracted from a grating - was neglected. This led to an overestimate of the resolving power of this spectrograph, especially in situations when the coherence length of the radiation under test is in the order ofmore » the effective aperture of the device. In conclusion, the limits of usability are shown here together with some measurements of known spectral lines.« less

Robust alignment of chromatograms by statistically analyzing the shifts matrix generated by moving window fast Fourier transform cross-correlation.

PubMed

Zhang, Mingjing; Wen, Ming; Zhang, Zhi-Min; Lu, Hongmei; Liang, Yizeng; Zhan, Dejian

2015-03-01

Retention time shift is one of the most challenging problems during the preprocessing of massive chromatographic datasets. Here, an improved version of the moving window fast Fourier transform cross-correlation algorithm is presented to perform nonlinear and robust alignment of chromatograms by analyzing the shifts matrix generated by moving window procedure. The shifts matrix in retention time can be estimated by fast Fourier transform cross-correlation with a moving window procedure. The refined shift of each scan point can be obtained by calculating the mode of corresponding column of the shifts matrix. This version is simple, but more effective and robust than the previously published moving window fast Fourier transform cross-correlation method. It can handle nonlinear retention time shift robustly if proper window size has been selected. The window size is the only one parameter needed to adjust and optimize. The properties of the proposed method are investigated by comparison with the previous moving window fast Fourier transform cross-correlation and recursive alignment by fast Fourier transform using chromatographic datasets. The pattern recognition results of a gas chromatography mass spectrometry dataset of metabolic syndrome can be improved significantly after preprocessing by this method. Furthermore, the proposed method is available as an open source package at https://github.com/zmzhang/MWFFT2. © 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

The short time Fourier transform and local signals

NASA Astrophysics Data System (ADS)

Okumura, Shuhei

In this thesis, I examine the theoretical properties of the short time discrete Fourier transform (STFT). The STFT is obtained by applying the Fourier transform by a fixed-sized, moving window to input series. We move the window by one time point at a time, so we have overlapping windows. I present several theoretical properties of the STFT, applied to various types of complex-valued, univariate time series inputs, and their outputs in closed forms. In particular, just like the discrete Fourier transform, the STFT's modulus time series takes large positive values when the input is a periodic signal. One main point is that a white noise time series input results in the STFT output being a complex-valued stationary time series and we can derive the time and time-frequency dependency structure such as the cross-covariance functions. Our primary focus is the detection of local periodic signals. I present a method to detect local signals by computing the probability that the squared modulus STFT time series has consecutive large values exceeding some threshold after one exceeding observation following one observation less than the threshold. We discuss a method to reduce the computation of such probabilities by the Box-Cox transformation and the delta method, and show that it works well in comparison to the Monte Carlo simulation method.

Studies on the binding behavior of prodigiosin with bovine hemoglobin by multi-spectroscopic techniques

NASA Astrophysics Data System (ADS)

Tang, Jing; Yang, Chao; Zhou, Lin; Ma, Fei; Liu, Shuchao; Wei, Shaohua; Zhou, Jiahong; Zhou, Yanhuai

2012-10-01

In this article, the interaction mechanism of prodigiosin (PG) with bovine hemoglobin (BHb) is studied in detail using various spectroscopic technologies. UV-vis absorption and fluorescence spectra demonstrate the interaction process. The Stern-Volmer plot and the time-resolved fluorescence study suggest the quenching mechanism of fluorescence of BHb by PG is a static quenching procedure, and the hydrophobic interactions play a major role in binding of PG to BHb. Furthermore, synchronous fluorescence studies, Fourier transform infrared (FTIR) and circular dichroism (CD) spectra reveal that the conformation of BHb is changed after conjugation with PG.

Long-distance super-resolution imaging assisted by enhanced spatial Fourier transform.

PubMed

Tang, Heng-He; Liu, Pu-Kun

2015-09-07

A new gradient-index (GRIN) lens that can realize enhanced spatial Fourier transform (FT) over optically long distances is demonstrated. By using an anisotropic GRIN metamaterial with hyperbolic dispersion, evanescent wave in free space can be transformed into propagating wave in the metamaterial and then focused outside due to negative-refraction. Both the results based on the ray tracing and the finite element simulation show that the spatial frequency bandwidth of the spatial FT can be extended to 2.7k(0) (k(0) is the wave vector in free space). Furthermore, assisted by the enhanced spatial FT, a new long-distance (in the optical far-field region) super-resolution imaging scheme is also proposed and the super resolved capability of λ/5 (λ is the wavelength in free space) is verified. The work may provide technical support for designing new-type high-speed microscopes with long working distances.

Application of phase correction to improve the interpretation of crude oil spectra obtained using 7 T Fourier transform ion cyclotron resonance mass spectrometry.

PubMed

Cho, Yunju; Qi, Yulin; O'Connor, Peter B; Barrow, Mark P; Kim, Sunghwan

2014-01-01

In this study, a phase-correction technique was applied to the study of crude oil spectra obtained using a 7 T Fourier transform ion cyclotron resonance mass spectrometry (FT-ICR MS). 7 T FT-ICR MS had not been widely used for oil analysis due to the lower resolving power compared with high field FT-ICR MS. For low field instruments, usage of data that has not been phase-corrected results in an inability to resolve critical mass splits of C3 and SH4 (3.4 mDa), and (13)C and CH (4.5 mDa). This results in incorrect assignments of molecular formulae, and discontinuous double bond equivalents (DBE) and carbon number distributions of S1, S2, and hydrocarbon classes are obtained. Application of phase correction to the same data, however, improves the reliability of assignments and produces continuous DBE and carbon number distributions. Therefore, this study clearly demonstrates that phase correction improves data analysis and the reliability of assignments of molecular formulae in crude oil anlayses.

Intermolecular dynamics of substitued benzene and cyclohexane liquids, studied by femtosecond nonlinear-optical polarization spectroscopy

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chang, Y.J.; Castner, E.W. Jr.

Femtosecond time-resolved optical-heterodyne detected Raman-induced Kerr effect spectroscopy (OHD-RIKES) is shown to be a powerful and comprehensive tool for studying the intermolecular dynamics occurring in liquids. The observed dynamics include both the underdamped or coherent inertial motions, and the longer time scale diffusive relaxation. The inertial dynamics include phonon-like intermolecular vibrations, intermolecular collisions, and librational caging motions. Data are presented and analyzed for a series of five liquids: cyclohexane, methylcyclohexane, toluene, benzyl alcohol, and benzonitrile, listed in order of increasing polarity. We explore the effects of aromaticity (e.g., methylcyclohexane vs toluene), symmetry reduction (cyclohexane vs methylcyclohexane), and substitution effects (e.g.,more » substituted benzene series) on the ultrafast intermolecular dynamics, for a group of molecular liquids of similar size and volume. We analyze the intermolecular dynamics in both the time and frequency domains by means of Fourier transformations. When Fourier-transformed into the frequency domain, the OHD-RIKES ultrafast transients of the intermolecular dynamics can be directly compared with the frequency domain spectra obtained from the far-infrared absorption and depolarized Raman techniques. This is done using the Gaussian librational caging model of Lynden-Bell and Steele, which results in a power-law scaling relation between dipole and polarizability time correlation functions. 122 refs., 7 figs., 7 tabs.« less

Time-Resolved Kinetic Chirped-Pulse Rotational Spectroscopy in a Room-Temperature Flow Reactor

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zaleski, Daniel P.; Harding, Lawrence B.; Klippenstein, Stephen J.

Chirped-pulse Fourier transform millimeter-wave spectroscopy is a potentially powerful tool for studying chemical reaction dynamics and kinetics. Branching ratios of multiple reaction products and intermediates can be measured with unprecedented chemical specificity; molecular isomers, conformers, and vibrational states have distinct rotational spectra. Here we demonstrate chirped-pulse spectroscopy of vinyl cyanide photoproducts in a flow tube reactor at ambient temperature of 295 K and pressures of 1-10 mu bar. This in situ and time-resolved experiment illustrates the utility of this novel approach to investigating chemical reaction dynamics and kinetics. Following 193 nm photodissociation of CH2CHCN, we observe rotational relaxation of energizedmore » HCN, HNC, and HCCCN photoproducts with 10 mu s time resolution and sample the vibrational population distribution of HCCCN. The experimental branching ratio HCN/HCCCN is compared with a model based on RRKM theory using high-level ab initio calculations, which were in turn validated by comparisons to Active Thermochemical Tables enthalpies.« less

Time-Resolved Kinetic Chirped-Pulse Rotational Spectroscopy in a Room-Temperature Flow Reactor

DOE PAGES

Zaleski, Daniel P.; Harding, Lawrence B.; Klippenstein, Stephen J.; ...

2017-12-01

Chirped-pulse Fourier transform millimeter-wave spectroscopy is a potentially powerful tool for studying chemical reaction dynamics and kinetics. Branching ratios of multiple reaction products and intermediates can be measured with unprecedented chemical specificity; molecular isomers, conformers, and vibrational states have distinct rotational spectra. Here we demonstrate chirped-pulse spectroscopy of vinyl cyanide photoproducts in a flow tube reactor at ambient temperature of 295 K and pressures of 1-10 mu bar. This in situ and time-resolved experiment illustrates the utility of this novel approach to investigating chemical reaction dynamics and kinetics. Following 193 nm photodissociation of CH2CHCN, we observe rotational relaxation of energizedmore » HCN, HNC, and HCCCN photoproducts with 10 mu s time resolution and sample the vibrational population distribution of HCCCN. The experimental branching ratio HCN/HCCCN is compared with a model based on RRKM theory using high-level ab initio calculations, which were in turn validated by comparisons to Active Thermochemical Tables enthalpies.« less

Analytical properties of time-of-flight PET data.

PubMed

Cho, Sanghee; Ahn, Sangtae; Li, Quanzheng; Leahy, Richard M

2008-06-07

We investigate the analytical properties of time-of-flight (TOF) positron emission tomography (PET) sinograms, where the data are modeled as line integrals weighted by a spatially invariant TOF kernel. First, we investigate the Fourier transform properties of 2D TOF data and extend the 'bow-tie' property of the 2D Radon transform to the time-of-flight case. Second, we describe a new exact Fourier rebinning method, TOF-FOREX, based on the Fourier transform in the time-of-flight variable. We then combine TOF-FOREX rebinning with a direct extension of the projection slice theorem to TOF data, to perform fast 3D TOF PET image reconstruction. Finally, we illustrate these properties using simulated data.

Analytical properties of time-of-flight PET data

NASA Astrophysics Data System (ADS)

Cho, Sanghee; Ahn, Sangtae; Li, Quanzheng; Leahy, Richard M.

2008-06-01

We investigate the analytical properties of time-of-flight (TOF) positron emission tomography (PET) sinograms, where the data are modeled as line integrals weighted by a spatially invariant TOF kernel. First, we investigate the Fourier transform properties of 2D TOF data and extend the 'bow-tie' property of the 2D Radon transform to the time-of-flight case. Second, we describe a new exact Fourier rebinning method, TOF-FOREX, based on the Fourier transform in the time-of-flight variable. We then combine TOF-FOREX rebinning with a direct extension of the projection slice theorem to TOF data, to perform fast 3D TOF PET image reconstruction. Finally, we illustrate these properties using simulated data.

High Accuracy Evaluation of the Finite Fourier Transform Using Sampled Data

NASA Technical Reports Server (NTRS)

Morelli, Eugene A.

1997-01-01

Many system identification and signal processing procedures can be done advantageously in the frequency domain. A required preliminary step for this approach is the transformation of sampled time domain data into the frequency domain. The analytical tool used for this transformation is the finite Fourier transform. Inaccuracy in the transformation can degrade system identification and signal processing results. This work presents a method for evaluating the finite Fourier transform using cubic interpolation of sampled time domain data for high accuracy, and the chirp Zeta-transform for arbitrary frequency resolution. The accuracy of the technique is demonstrated in example cases where the transformation can be evaluated analytically. Arbitrary frequency resolution is shown to be important for capturing details of the data in the frequency domain. The technique is demonstrated using flight test data from a longitudinal maneuver of the F-18 High Alpha Research Vehicle.

3-D surface profilometry based on modulation measurement by applying wavelet transform method

NASA Astrophysics Data System (ADS)

Zhong, Min; Chen, Feng; Xiao, Chao; Wei, Yongchao

2017-01-01

A new analysis of 3-D surface profilometry based on modulation measurement technique by the application of Wavelet Transform method is proposed. As a tool excelling for its multi-resolution and localization in the time and frequency domains, Wavelet Transform method with good localized time-frequency analysis ability and effective de-noizing capacity can extract the modulation distribution more accurately than Fourier Transform method. Especially for the analysis of complex object, more details of the measured object can be well remained. In this paper, the theoretical derivation of Wavelet Transform method that obtains the modulation values from a captured fringe pattern is given. Both computer simulation and elementary experiment are used to show the validity of the proposed method by making a comparison with the results of Fourier Transform method. The results show that the Wavelet Transform method has a better performance than the Fourier Transform method in modulation values retrieval.

Rapid 3D NMR using the filter diagonalization method: application to oligosaccharides derivatized with 13C-labeled acetyl groups

NASA Astrophysics Data System (ADS)

Armstrong, Geoffrey S.; Cano, Kristin E.; Mandelshtam, Vladimir A.; Shaka, A. J.; Bendiak, Brad

2004-09-01

Rapid 3D NMR spectroscopy of oligosaccharides having isotopically labeled acetyl "isotags" was made possible with high resolution in the indirect dimensions using the filter diagonalization method (FDM). A pulse sequence was designed for the optimal correlation of acetyl methyl protons, methyl carbons, and carbonyl carbons. The multi-dimensional nature of the FDM, coupled with the advantages of constant-time evolution periods, resulted in marked improvements over Fourier transform (FT) and mirror-image linear prediction (MI-LP) processing methods. The three methods were directly compared using identical data sets. A highly resolved 3D spectrum was achieved with the FDM using a very short experimental time (28 min).

Rapid 3D NMR using the filter diagonalization method: application to oligosaccharides derivatized with 13C-labeled acetyl groups.

PubMed

Armstrong, Geoffrey S; Cano, Kristin E; Mandelshtam, Vladimir A; Shaka, A J; Bendiak, Brad

2004-09-01

Rapid 3D NMR spectroscopy of oligosaccharides having isotopically labeled acetyl "isotags" was made possible with high resolution in the indirect dimensions using the filter diagonalization method (FDM). A pulse sequence was designed for the optimal correlation of acetyl methyl protons, methyl carbons, and carbonyl carbons. The multi-dimensional nature of the FDM, coupled with the advantages of constant-time evolution periods, resulted in marked improvements over Fourier transform (FT) and mirror-image linear prediction (MI-LP) processing methods. The three methods were directly compared using identical data sets. A highly resolved 3D spectrum was achieved with the FDM using a very short experimental time (28 min).

Coherent time-stretch transformation for real-time capture of wideband signals.

PubMed

Buckley, Brandon W; Madni, Asad M; Jalali, Bahram

2013-09-09

Time stretch transformation of wideband waveforms boosts the performance of analog-to-digital converters and digital signal processors by slowing down analog electrical signals before digitization. The transform is based on dispersive Fourier transformation implemented in the optical domain. A coherent receiver would be ideal for capturing the time-stretched optical signal. Coherent receivers offer improved sensitivity, allow for digital cancellation of dispersion-induced impairments and optical nonlinearities, and enable decoding of phase-modulated optical data formats. Because time-stretch uses a chirped broadband (>1 THz) optical carrier, a new coherent detection technique is required. In this paper, we introduce and demonstrate coherent time stretch transformation; a technique that combines dispersive Fourier transform with optically broadband coherent detection.

Synthesis and characterization of a new photoluminescent material, tris-[1-10 phenanthroline] aluminium

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kumar, Rahul, E-mail: id-kumarrahul003@gmail.com; Bhargava, Parag; Dvivedi, Avanish

A new photoluminescent material namely tris-[1-10 Phenanthroline] Aluminium Al(Phen){sub 3} has been synthesized and characterized. This material was characterized by fourier transform infrared spectroscopy (FTIR),nuclear magnetic resonance (NMR),mass spectroscopy, thermal gravimetric analysis (TGA),ultraviolet-visible spectroscopy(UV) and photoluminescence (PL). This material shows thermal stability up to 300°C. This material showed absorption maxima at 352nm which may be attributed to the moderate energy (π–π{sup *}) transition. Photoluminescence spectra for this material showed the most intense peak at 423 nm and the time resolved photoluminescence spectra showed two life time components. The decay times of the first and second component were 1.4ns and 4.8 ns respectively.

Building a symbolic computer algebra toolbox to compute 2D Fourier transforms in polar coordinates.

PubMed

Dovlo, Edem; Baddour, Natalie

2015-01-01

The development of a symbolic computer algebra toolbox for the computation of two dimensional (2D) Fourier transforms in polar coordinates is presented. Multidimensional Fourier transforms are widely used in image processing, tomographic reconstructions and in fact any application that requires a multidimensional convolution. By examining a function in the frequency domain, additional information and insights may be obtained. The advantages of our method include: •The implementation of the 2D Fourier transform in polar coordinates within the toolbox via the combination of two significantly simpler transforms.•The modular approach along with the idea of lookup tables implemented help avoid the issue of indeterminate results which may occur when attempting to directly evaluate the transform.•The concept also helps prevent unnecessary computation of already known transforms thereby saving memory and processing time.

Detection of Fast Moving and Accelerating Targets Compensating Range and Doppler Migration

DTIC Science & Technology

2014-06-01

Radon -Fourier transform has been introduced to realize long- term coherent integration of the moving targets with range migration [8, 9]. Radon ...2010) Long-time coherent integration for radar target detection base on Radon -Fourier transform, in Proceedings of the IEEE Radar Conference, pp...432–436. 9. Xu, J., Yu, J., Peng, Y. & Xia, X. (2011) Radon -Fourier transform for radar target detection, I: Generalized Doppler filter bank, IEEE

Analytical Properties of Time-of-Flight PET Data

PubMed Central

Cho, Sanghee; Ahn, Sangtae; Li, Quanzheng; Leahy, Richard M.

2015-01-01

We investigate the analytical properties of time-of-flight (TOF) positron emission tomography (PET) sinograms, where the data are modeled as line integrals weighted by a spatially invariant TOF kernel. First, we investigate the Fourier transform properties of 2D TOF data and extend the “bow-tie” property of the 2D Radon transform to the time of flight case. Second, we describe a new exact Fourier rebinning method, TOF-FOREX, based on the Fourier transform in the time-of-flight variable. We then combine TOF-FOREX rebinning with a direct extension of the projection slice theorem to TOF data, to perform fast 3D TOF PET image reconstruction. Finally, we illustrate these properties using simulated data. PMID:18460746

Fourier transform of delayed fluorescence as an indicator of herbicide concentration.

PubMed

Guo, Ya; Tan, Jinglu

2014-12-21

It is well known that delayed fluorescence (DF) from Photosystem II (PSII) of plant leaves can be potentially used to sense herbicide pollution and evaluate the effect of herbicides on plant leaves. The research of using DF as a measure of herbicides in the literature was mainly conducted in time domain and qualitative correlation was often obtained. Fourier transform is often used to analyze signals. Viewing DF signal in frequency domain through Fourier transform may allow separation of signal components and provide a quantitative method for sensing herbicides. However, there is a lack of an attempt to use Fourier transform of DF as an indicator of herbicide. In this work, the relationship between the Fourier transform of DF and herbicide concentration was theoretically modelled and analyzed, which immediately yielded a quantitative method to measure herbicide concentration in frequency domain. Experiments were performed to validate the developed method. Copyright © 2014 Elsevier Ltd. All rights reserved.

Time-resolved fuel injector flow characterisation based on 3D laser Doppler vibrometry

NASA Astrophysics Data System (ADS)

Crua, Cyril; Heikal, Morgan R.

2014-12-01

Hydrodynamic turbulence and cavitation are known to play a significant role in high-pressure atomizers, but the small geometries and extreme operating conditions hinder the understanding of the flow’s characteristics. Diesel internal flow experiments are generally conducted using x-ray techniques or on transparent, and often enlarged, nozzles with different orifice geometries and surface roughness to those found in production injectors. In order to enable investigations of the fuel flow inside unmodified injectors, we have developed a new experimental approach to measure time-resolved vibration spectra of diesel nozzles using a 3D laser vibrometer. The technique we propose is based on the triangulation of the vibrometer and fuel pressure transducer signals, and enables the quantitative characterisation of quasi-cyclic internal flows without requiring modifications to the injector, the working fluid, or limiting the fuel injection pressure. The vibrometer, which uses the Doppler effect to measure the velocity of a vibrating object, was used to scan injector nozzle tips during the injection event. The data were processed using a discrete Fourier transform to provide time-resolved spectra for valve-closed-orifice, minisac and microsac nozzle geometries, and injection pressures ranging from 60 to 160 MPa, hence offering unprecedented insight into cyclic cavitation and internal mechanical dynamic processes. A peak was consistently found in the spectrograms between 6 and 7.5 kHz for all nozzles and injection pressures. Further evidence of a similar spectral peak was obtained from the fuel pressure transducer and a needle lift sensor mounted into the injector body. Evidence of propagation of the nozzle oscillations to the liquid sprays was obtained by recording high-speed videos of the near-nozzle diesel jet, and computing the fast Fourier transform for a number of pixel locations at the interface of the jets. This 6-7.5 kHz frequency peak is proposed to be the natural frequency for the injector’s main internal fuel line. Other spectral peaks were found between 35 and 45 kHz for certain nozzle geometries, suggesting that these particular frequencies may be linked to nozzle dependent cavitation phenomena.

Feature Extraction for Bearing Prognostics and Health Management (PHM) - A Survey (Preprint)

DTIC Science & Technology

2008-05-01

Envelope analysis • Cepstrum analysis • Higher order spectrum • Short-time Fourier Transform (STFT) • Wigner - Ville distribution ( WVD ) • Empirical mode...techniques are the short-time Fourier transform (STFT), the Wigner - Ville distribution , and the wavelet transform. In this paper we categorize wavelets...diagnosis have shown in many publications, for example, [22]. b) Wigner – Ville distribution : The afore-mentioned STFT is conceptually simple. However

A novel recursive Fourier transform for nonuniform sampled signals: application to heart rate variability spectrum estimation.

PubMed

Holland, Alexander; Aboy, Mateo

2009-07-01

We present a novel method to iteratively calculate discrete Fourier transforms for discrete time signals with sample time intervals that may be widely nonuniform. The proposed recursive Fourier transform (RFT) does not require interpolation of the samples to uniform time intervals, and each iterative transform update of N frequencies has computational order N. Because of the inherent non-uniformity in the time between successive heart beats, an application particularly well suited for this transform is power spectral density (PSD) estimation for heart rate variability. We compare RFT based spectrum estimation with Lomb-Scargle Transform (LST) based estimation. PSD estimation based on the LST also does not require uniform time samples, but the LST has a computational order greater than Nlog(N). We conducted an assessment study involving the analysis of quasi-stationary signals with various levels of randomly missing heart beats. Our results indicate that the RFT leads to comparable estimation performance to the LST with significantly less computational overhead and complexity for applications requiring iterative spectrum estimations.

The Use of Continuous Wavelet Transform Based on the Fast Fourier Transform in the Analysis of Multi-channel Electrogastrography Recordings.

PubMed

Komorowski, Dariusz; Pietraszek, Stanislaw

2016-01-01

This paper presents the analysis of multi-channel electrogastrographic (EGG) signals using the continuous wavelet transform based on the fast Fourier transform (CWTFT). The EGG analysis was based on the determination of the several signal parameters such as dominant frequency (DF), dominant power (DP) and index of normogastria (NI). The use of continuous wavelet transform (CWT) allows for better visible localization of the frequency components in the analyzed signals, than commonly used short-time Fourier transform (STFT). Such an analysis is possible by means of a variable width window, which corresponds to the scale time of observation (analysis). Wavelet analysis allows using long time windows when we need more precise low-frequency information, and shorter when we need high frequency information. Since the classic CWT transform requires considerable computing power and time, especially while applying it to the analysis of long signals, the authors used the CWT analysis based on the fast Fourier transform (FFT). The CWT was obtained using properties of the circular convolution to improve the speed of calculation. This method allows to obtain results for relatively long records of EGG in a fairly short time, much faster than using the classical methods based on running spectrum analysis (RSA). In this study authors indicate the possibility of a parametric analysis of EGG signals using continuous wavelet transform which is the completely new solution. The results obtained with the described method are shown in the example of an analysis of four-channel EGG recordings, performed for a non-caloric meal.

Building a symbolic computer algebra toolbox to compute 2D Fourier transforms in polar coordinates

PubMed Central

Dovlo, Edem; Baddour, Natalie

2015-01-01

The development of a symbolic computer algebra toolbox for the computation of two dimensional (2D) Fourier transforms in polar coordinates is presented. Multidimensional Fourier transforms are widely used in image processing, tomographic reconstructions and in fact any application that requires a multidimensional convolution. By examining a function in the frequency domain, additional information and insights may be obtained. The advantages of our method include: • The implementation of the 2D Fourier transform in polar coordinates within the toolbox via the combination of two significantly simpler transforms. • The modular approach along with the idea of lookup tables implemented help avoid the issue of indeterminate results which may occur when attempting to directly evaluate the transform. • The concept also helps prevent unnecessary computation of already known transforms thereby saving memory and processing time. PMID:26150988

Ultra-broadband infrared pump-probe spectroscopy using synchrotron radiation and a tuneable pump.

PubMed

Carroll, Lee; Friedli, Peter; Lerch, Philippe; Schneider, Jörg; Treyer, Daniel; Hunziker, Stephan; Stutz, Stefan; Sigg, Hans

2011-06-01

Synchrotron infrared sources have become popular mainly because of their excellent broadband brilliance, which enables spectroscopically resolved spatial-mapping of stationary objects at the diffraction limit. In this article we focus on an often-neglected further advantage of such sources - their unique time-structure - to bring such broadband spectroscopy to the time domain, for studying dynamic phenomenon down to the 100 ps limit. We describe the ultra-broadband (12.5 to 1.1 μm) Fourier transform pump-probe setup, for condensed matter transmission- and reflection-spectroscopy, installed at the X01DC infrared beam-line of the Swiss Light Source (SLS). The optical pump consists of a widely tuneable 100 ps 1 kHz laser system, covering 94% of the 16 to 1.1 μm range. A thorough description of the system is given, including (i) the vector-modulator providing purely electronic tuning of the pump-probe overlap up to 1 ms with sub-ps time resolution, (ii) the 500 MHz data acquisition system interfaced with the experimental physics and industrial control system (EPICS) based SLS control system for consecutive pulse sampling, and (iii) the step-scan time-slice Fourier transform scheme for simultaneous recording of the dual-channel pumped, un-pumped, and difference spectra. The typical signal/noise ratio of a single interferogram in a 100 ps time slice is 300 (measured during one single 140 s TopUp period). This signal/noise ratio is comparable to that of existing gated Globar pump-probe Fourier transform spectroscopy, but brings up to four orders of magnitude better time resolution. To showcase the utility of broadband pump-probe spectroscopy, we investigate a Ge-on-Si material system similar to that in which optically pumped direct-gap lasing was recently reported. We show that the mid-infrared reflection-spectra can be used to determine the optically injected carrier density, while the mid- and near-infrared transmission-spectra can be used to separate the strong pump-induced absorption and inversion processes present at the direct-gap energy. © 2011 American Institute of Physics

A two-dimensional time domain near zone to far zone transformation

NASA Technical Reports Server (NTRS)

Luebbers, Raymond J.; Ryan, Deirdre; Beggs, John H.; Kunz, Karl S.

1991-01-01

A time domain transformation useful for extrapolating three dimensional near zone finite difference time domain (FDTD) results to the far zone was presented. Here, the corresponding two dimensional transform is outlined. While the three dimensional transformation produced a physically observable far zone time domain field, this is not convenient to do directly in two dimensions, since a convolution would be required. However, a representative two dimensional far zone time domain result can be obtained directly. This result can then be transformed to the frequency domain using a Fast Fourier Transform, corrected with a simple multiplicative factor, and used, for example, to calculate the complex wideband scattering width of a target. If an actual time domain far zone result is required, it can be obtained by inverse Fourier transform of the final frequency domain result.

A two-dimensional time domain near zone to far zone transformation

NASA Technical Reports Server (NTRS)

Luebbers, Raymond J.; Ryan, Deirdre; Beggs, John H.; Kunz, Karl S.

1991-01-01

In a previous paper, a time domain transformation useful for extrapolating 3-D near zone finite difference time domain (FDTD) results to the far zone was presented. In this paper, the corresponding 2-D transform is outlined. While the 3-D transformation produced a physically observable far zone time domain field, this is not convenient to do directly in 2-D, since a convolution would be required. However, a representative 2-D far zone time domain result can be obtained directly. This result can then be transformed to the frequency domain using a Fast Fourier Transform, corrected with a simple multiplicative factor, and used, for example, to calculate the complex wideband scattering width of a target. If an actual time domain far zone result is required it can be obtained by inverse Fourier transform of the final frequency domain result.

Effect of pressure on infrared spectra of ice 7

NASA Technical Reports Server (NTRS)

Holzapfel, W. B.; Seiler, B.; Nicol, M.

1983-01-01

The effect of pressure on the infrared spectra of H2O and D2O ice VII was studied at room temperature and pressures between 2 and 15 GPa with a Fourier transform infrared spectrometer and a diamond anvil high pressure cell. Two librational modes, one bending mode, and various overtone bands are well resolved. The stretching modes, nu sub 1 and nu sub 3 are poorly resolved due to overlap with diamond window absorption. Differences between the spectra of H2O and D2O are discussed.

On the action of Heisenberg's uncertainty principle in discrete linear methods for calculating the components of the deflection of the vertical

NASA Astrophysics Data System (ADS)

Mazurova, Elena; Lapshin, Aleksey

2013-04-01

The method of discrete linear transformations that can be implemented through the algorithms of the Standard Fourier Transform (SFT), Short-Time Fourier Transform (STFT) or Wavelet transform (WT) is effective for calculating the components of the deflection of the vertical from discrete values of gravity anomaly. The SFT due to the action of Heisenberg's uncertainty principle indicates weak spatial localization that manifests in the following: firstly, it is necessary to know the initial digital signal on the complete number line (in case of one-dimensional transform) or in the whole two-dimensional space (if a two-dimensional transform is performed) in order to find the SFT. Secondly, the localization and values of the "peaks" of the initial function cannot be derived from its Fourier transform as the coefficients of the Fourier transform are formed by taking into account all the values of the initial function. Thus, the SFT gives the global information on all frequencies available in the digital signal throughout the whole time period. To overcome this peculiarity it is necessary to localize the signal in time and apply the Fourier transform only to a small portion of the signal; the STFT that differs from the SFT only by the presence of an additional factor (window) is used for this purpose. A narrow enough window is chosen to localize the signal in time and, according to Heisenberg's uncertainty principle, it results in have significant enough uncertainty in frequency. If one chooses a wide enough window it, according to the same principle, will increase time uncertainty. Thus, if the signal is narrowly localized in time its spectrum, on the contrary, is spread on the complete axis of frequencies, and vice versa. The STFT makes it possible to improve spatial localization, that is, it allows one to define the presence of any frequency in the signal and the interval of its presence. However, owing to Heisenberg's uncertainty principle, it is impossible to tell precisely, what frequency is present in the signal at the current moment of time: it is possible to speak only about the range of frequencies. Besides, it is impossible to specify precisely the time moment of the presence of this or that frequency: it is possible to speak only about the time frame. It is this feature that imposes major constrains on the applicability of the STFT. In spite of the fact that the problems of resolution in time and frequency result from a physical phenomenon (Heisenberg's uncertainty principle) and exist independent of the transform applied, there is a possibility to analyze any signal, using the alternative approach - the multiresolutional analysis (MRA). The wavelet-transform is one of the methods for making a MRA-type analysis. Thanks to it, low frequencies can be shown in a more detailed form with respect to time, and high ones - with respect to frequency. The paper presents the results of calculating of the components of the deflection of the vertical, done by the SFT, STFT and WT. The results are presented in the form of 3-d models that visually show the action of Heisenberg's uncertainty principle in the specified algorithms. The research conducted allows us to recommend the application of wavelet-transform to calculate of the components of the deflection of the vertical in the near-field zone. Keywords: Standard Fourier Transform, Short-Time Fourier Transform, Wavelet Transform, Heisenberg's uncertainty principle.

A Graphical Presentation to Teach the Concept of the Fourier Transform

ERIC Educational Resources Information Center

Besalu, E.

2006-01-01

A study was conducted to visualize the reason why the Fourier transform technique is useful to detect the originating frequencies of a complicated superposition of waves. The findings reveal that students respond well when instructors adapt pictorial presentation to show how the time-domain function is transformed into the frequency domain.

Dioxin analysis by gas chromatography-Fourier transform ion cyclotron resonance mass spectrometry (GC-FTICRMS).

PubMed

Taguchi, Vince Y; Nieckarz, Robert J; Clement, Ray E; Krolik, Stefan; Williams, Robert

2010-11-01

The feasibility of utilizing a gas chromatograph-tandem quadrupole-Fourier transform ion cyclotron resonance mass spectrometer (GC-MS/MS-FTICRMS) to analyze chlorinated-dioxins/furans (CDDs/CDFs) and mixed halogenated dioxins/furans (HDDs/HDFs) was investigated by operating the system in the GC-FTICRMS mode. CDDs/CDFs and mixed HDDs/HDFs could be analyzed at 50,000 to 100,000 resolving power (RP) on the capillary gas chromatographic time scale. Initial experiments demonstrated that 1 pg of 2,3,7,8-tetrachlorodibenzo-p-dioxin (TCDD) and 5 pg of 2-bromo-3,7,8-trichlorodibenzo-p-dioxin (BTrCDD) could be detected. The feasibility of utilizing an FTICRMS for screening of CDDs/CDFs, HDDs/HDFs and related compounds was also investigated by analyzing an extract from vegetation exposed to fall-out from an industrial fire. CDDs/CDFs, chlorinated pyrenes and chlorinated tetracenes could be detected from a Kendrick plot analysis of the ultrahigh resolution mass spectra. Mass accuracies were of the order of 0.5 ppm on standards with external mass calibration and 1 ppm on a sample with internal mass calibration. Copyright © 2010 American Society for Mass Spectrometry. Published by Elsevier Inc. All rights reserved.

Vibrational analysis of carbonyl modes in different stages of light-induced cyclopyrimidine dimer repair reactions

NASA Astrophysics Data System (ADS)

Schmitz, Matthias; Tavan, Paul; Nonella, Marco

2001-11-01

The formation of cyclopyrimidine dimers is a DNA defect, which is repaired by the enzyme DNA photolyase in a light-induced reaction. Radical anions of the dimers have been suggested to occur as short-lived intermediates during repair. For their identification time-resolved Fourier-transform infrared (FTIR) spectroscopy will be a method of choice. To support and guide such spectroscopic studies we have calculated the vibrational spectra of various pyrimidine compounds using density functional methods. Our results suggest that the carbonyl vibrations of these molecules can serve as marker modes to identify and distinguish intermediates of the repair reaction.

Wavelets

NASA Astrophysics Data System (ADS)

Strang, Gilbert

1994-06-01

Several methods are compared that are used to analyze and synthesize a signal. Three ways are mentioned to transform a symphony: into cosine waves (Fourier transform), into pieces of cosines (short-time Fourier transform), and into wavelets (little waves that start and stop). Choosing the best basis, higher dimensions, fast wavelet transform, and Daubechies wavelets are discussed. High-definition television is described. The use of wavelets in identifying fingerprints in the future is related.

Fast Fourier Transform Spectral Analysis Program

NASA Technical Reports Server (NTRS)

Daniel, J. A., Jr.; Graves, M. L.; Hovey, N. M.

1969-01-01

Fast Fourier Transform Spectral Analysis Program is used in frequency spectrum analysis of postflight, space vehicle telemetered trajectory data. This computer program with a digital algorithm can calculate power spectrum rms amplitudes and cross spectrum of sampled parameters at even time increments.

Matching-pursuit/split-operator-Fourier-transform computations of thermal correlation functions.

PubMed

Chen, Xin; Wu, Yinghua; Batista, Victor S

2005-02-08

A rigorous and practical methodology for evaluating thermal-equilibrium density matrices, finite-temperature time-dependent expectation values, and time-correlation functions is described. The method involves an extension of the matching-pursuit/split-operator-Fourier-transform method to the solution of the Bloch equation via imaginary-time propagation of the density matrix and the evaluation of Heisenberg time-evolution operators through real-time propagation in dynamically adaptive coherent-state representations.

A FOURIER-TRANSFORMED BREMSSTRAHLUNG FLASH MODEL FOR THE PRODUCTION OF X-RAY TIME LAGS IN ACCRETING BLACK HOLE SOURCES

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kroon, John J.; Becker, Peter A., E-mail: jkroon@gmu.edu, E-mail: pbecker@gmu.edu

Accreting black hole sources show a wide variety of rapid time variability, including the manifestation of time lags during X-ray transients, in which a delay (phase shift) is observed between the Fourier components of the hard and soft spectra. Despite a large body of observational evidence for time lags, no fundamental physical explanation for the origin of this phenomenon has been presented. We develop a new theoretical model for the production of X-ray time lags based on an exact analytical solution for the Fourier transform describing the diffusion and Comptonization of seed photons propagating through a spherical corona. The resultingmore » Green's function can be convolved with any source distribution to compute the associated Fourier transform and time lags, hence allowing us to explore a wide variety of injection scenarios. We show that thermal Comptonization is able to self-consistently explain both the X-ray time lags and the steady-state (quiescent) X-ray spectrum observed in the low-hard state of Cyg X-1. The reprocessing of bremsstrahlung seed photons produces X-ray time lags that diminish with increasing Fourier frequency, in agreement with the observations for a wide range of sources.« less

Artifacts in time-resolved Kelvin probe force microscopy

DOE PAGES

Sadewasser, Sascha; Nicoara, Nicoleta; Solares, Santiago D.

2018-04-24

Kelvin probe force microscopy (KPFM) has been used for the characterization of metals, insulators, and semiconducting materials on the nanometer scale. Especially in semiconductors, the charge dynamics are of high interest. Recently, several techniques for time-resolved measurements with time resolution down to picoseconds have been developed, many times using a modulated excitation signal, e.g. light modulation or bias modulation that induces changes in the charge carrier distribution. For fast modulation frequencies, the KPFM controller measures an average surface potential, which contains information about the involved charge carrier dynamics. Here, we show that such measurements are prone to artifacts due tomore » frequency mixing, by performing numerical dynamics simulations of the cantilever oscillation in KPFM subjected to a bias-modulated signal. For square bias pulses, the resulting time-dependent electrostatic forces are very complex and result in intricate mixing of frequencies that may, in some cases, have a component at the detection frequency, leading to falsified KPFM measurements. Additionally, we performed fast Fourier transform (FFT) analyses that match the results of the numerical dynamics simulations. Small differences are observed that can be attributed to transients and higher-order Fourier components, as a consequence of the intricate nature of the cantilever driving forces. These results are corroborated by experimental measurements on a model system. In the experimental case, additional artifacts are observed due to constructive or destructive interference of the bias modulation with the cantilever oscillation. Also, in the case of light modulation, we demonstrate artifacts due to unwanted illumination of the photodetector of the beam deflection detection system. Lastly, guidelines for avoiding such artifacts are given.« less

Artifacts in time-resolved Kelvin probe force microscopy

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sadewasser, Sascha; Nicoara, Nicoleta; Solares, Santiago D.

Kelvin probe force microscopy (KPFM) has been used for the characterization of metals, insulators, and semiconducting materials on the nanometer scale. Especially in semiconductors, the charge dynamics are of high interest. Recently, several techniques for time-resolved measurements with time resolution down to picoseconds have been developed, many times using a modulated excitation signal, e.g. light modulation or bias modulation that induces changes in the charge carrier distribution. For fast modulation frequencies, the KPFM controller measures an average surface potential, which contains information about the involved charge carrier dynamics. Here, we show that such measurements are prone to artifacts due tomore » frequency mixing, by performing numerical dynamics simulations of the cantilever oscillation in KPFM subjected to a bias-modulated signal. For square bias pulses, the resulting time-dependent electrostatic forces are very complex and result in intricate mixing of frequencies that may, in some cases, have a component at the detection frequency, leading to falsified KPFM measurements. Additionally, we performed fast Fourier transform (FFT) analyses that match the results of the numerical dynamics simulations. Small differences are observed that can be attributed to transients and higher-order Fourier components, as a consequence of the intricate nature of the cantilever driving forces. These results are corroborated by experimental measurements on a model system. In the experimental case, additional artifacts are observed due to constructive or destructive interference of the bias modulation with the cantilever oscillation. Also, in the case of light modulation, we demonstrate artifacts due to unwanted illumination of the photodetector of the beam deflection detection system. Lastly, guidelines for avoiding such artifacts are given.« less

Difference structures from time-resolved small-angle and wide-angle x-ray scattering

NASA Astrophysics Data System (ADS)

Nepal, Prakash; Saldin, D. K.

2018-05-01

Time-resolved small-angle x-ray scattering/wide-angle x-ray scattering (SAXS/WAXS) is capable of recovering difference structures directly from difference SAXS/WAXS curves. It does so by means of the theory described here because the structural changes in pump-probe detection in a typical time-resolved experiment are generally small enough to be confined to a single residue or group in close proximity which is identified by a method akin to the difference Fourier method of time-resolved crystallography. If it is assumed, as is usual with time-resolved structures, that the moved atoms lie within the residue, the 100-fold reduction in the search space (assuming a typical protein has about 100 residues) allows the exaction of the structure by a simulated annealing algorithm with a huge reduction in computing time and leads to a greater resolution by varying the positions of atoms only within that residue. This reduction in the number of potential moved atoms allows us to identify the actual motions of the individual atoms. In the case of a crystal, time-resolved calculations are normally performed using the difference Fourier method, which is, of course, not directly applicable to SAXS/WAXS. The method developed in this paper may be thought of as a substitute for that method which allows SAXS/WAXS (and hence disordered molecules) to also be used for time-resolved structural work.

Signal processing applications of massively parallel charge domain computing devices

NASA Technical Reports Server (NTRS)

Fijany, Amir (Inventor); Barhen, Jacob (Inventor); Toomarian, Nikzad (Inventor)

1999-01-01

The present invention is embodied in a charge coupled device (CCD)/charge injection device (CID) architecture capable of performing a Fourier transform by simultaneous matrix vector multiplication (MVM) operations in respective plural CCD/CID arrays in parallel in O(1) steps. For example, in one embodiment, a first CCD/CID array stores charge packets representing a first matrix operator based upon permutations of a Hartley transform and computes the Fourier transform of an incoming vector. A second CCD/CID array stores charge packets representing a second matrix operator based upon different permutations of a Hartley transform and computes the Fourier transform of an incoming vector. The incoming vector is applied to the inputs of the two CCD/CID arrays simultaneously, and the real and imaginary parts of the Fourier transform are produced simultaneously in the time required to perform a single MVM operation in a CCD/CID array.

Femtosecond dynamics in hydrogen-bonded solvents

DOE Office of Scientific and Technical Information (OSTI.GOV)

Castner, E.W. Jr.; Chang, Y.J.

1993-09-01

We present results on the ultrafast dynamics of pure hydrogen-bonding solvents, obtained using femtosecond Fourier-transform optical-heterodyne-detected, Raman-induced Kerr effect spectroscopy. Solvent systems we have studied include the formamides, water, ethylene glycol, and acetic acid. Inertial and diffusive motions are clearly resolved. We comment on the effect that such ultrafast solvent motions have on chemical reactions in solution.

Contribution made by multivariate curve resolution applied to gel permeation chromatography-Fourier transform infrared data for an in-depth characterization of styrene-butadiene rubber blends.

PubMed

Ruckebusch, C; Vilmin, F; Coste, N; Huvenne, J P

2008-07-01

We evaluate the contribution made by multivariate curve resolution-alternating least squares (MCR-ALS) for resolving gel permeation chromatography-Fourier transform infrared (GPC-FT-IR) data collected on butadiene rubber (BR) and styrene butadiene rubber (SBR) blends in order to access in-depth knowledge of polymers along the molecular weight distribution (MWD). In the BR-SBR case, individual polymers differ in chemical composition but share almost the same MWD. Principal component analysis (PCA) gives a general overview of the data structure and attests to the feasibility of modeling blends as a binary system. MCR-ALS is then performed. It allows resolving the chromatographic coelution and validates the chosen methodology. For SBR-SBR blends, the problem is more challenging since the individual elastomers present the same chemical composition. Rank deficiency is detected from the PCA data structure analysis. MCR-ALS is thus performed on column-wise augmented matrices. It brings very useful insight into the composition of the analyzed blends. In particular, a weak change in the composition of individual SBR in the MWD's lowest mass region is revealed.

Spectral analysis for GNSS coordinate time series using chirp Fourier transform

NASA Astrophysics Data System (ADS)

Feng, Shengtao; Bo, Wanju; Ma, Qingzun; Wang, Zifan

2017-12-01

Spectral analysis for global navigation satellite system (GNSS) coordinate time series provides a principal tool to understand the intrinsic mechanism that affects tectonic movements. Spectral analysis methods such as the fast Fourier transform, Lomb-Scargle spectrum, evolutionary power spectrum, wavelet power spectrum, etc. are used to find periodic characteristics in time series. Among spectral analysis methods, the chirp Fourier transform (CFT) with less stringent requirements is tested with synthetic and actual GNSS coordinate time series, which proves the accuracy and efficiency of the method. With the length of series only limited to even numbers, CFT provides a convenient tool for windowed spectral analysis. The results of ideal synthetic data prove CFT accurate and efficient, while the results of actual data show that CFT is usable to derive periodic information from GNSS coordinate time series.

Compressed-sensing wavenumber-scanning interferometry

NASA Astrophysics Data System (ADS)

Bai, Yulei; Zhou, Yanzhou; He, Zhaoshui; Ye, Shuangli; Dong, Bo; Xie, Shengli

2018-01-01

The Fourier transform (FT), the nonlinear least-squares algorithm (NLSA), and eigenvalue decomposition algorithm (EDA) are used to evaluate the phase field in depth-resolved wavenumber-scanning interferometry (DRWSI). However, because the wavenumber series of the laser's output is usually accompanied by nonlinearity and mode-hop, FT, NLSA, and EDA, which are only suitable for equidistant interference data, often lead to non-negligible phase errors. In this work, a compressed-sensing method for DRWSI (CS-DRWSI) is proposed to resolve this problem. By using the randomly spaced inverse Fourier matrix and solving the underdetermined equation in the wavenumber domain, CS-DRWSI determines the nonuniform sampling and spectral leakage of the interference spectrum. Furthermore, it can evaluate interference data without prior knowledge of the object. The experimental results show that CS-DRWSI improves the depth resolution and suppresses sidelobes. It can replace the FT as a standard algorithm for DRWSI.

Indium hydroxide to oxide decomposition observed in one nanocrystal during in situ transmission electron microscopy studies

DOE Office of Scientific and Technical Information (OSTI.GOV)

Miehe, Gerhard; Lauterbach, Stefan; Kleebe, Hans-Joachim

The high-resolution transmission electron microscopy (HR-TEM) is used to study, in situ, spatially resolved decomposition in individual nanocrystals of metal hydroxides and oxyhydroxides. This case study reports on the decomposition of indium hydroxide (c-In(OH){sub 3}) to bixbyite-type indium oxide (c-In{sub 2}O{sub 3}). The electron beam is focused onto a single cube-shaped In(OH){sub 3} crystal of {l_brace}100{r_brace} morphology with ca. 35 nm edge length and a sequence of HR-TEM images was recorded during electron beam irradiation. The frame-by-frame analysis of video sequences allows for the in situ, time-resolved observation of the shape and orientation of the transformed crystals, which in turnmore » enables the evaluation of the kinetics of c-In{sub 2}O{sub 3} crystallization. Supplementary material (video of the transformation) related to this article can be found online at (10.1016/j.jssc.2012.09.022). After irradiation the shape of the parent cube-shaped crystal is preserved, however, its linear dimension (edge) is reduced by the factor 1.20. The corresponding spotted selected area electron diffraction (SAED) pattern representing zone [001] of c-In(OH){sub 3} is transformed to a diffuse strongly textured ring-like pattern of c-In{sub 2}O{sub 3} that indicates the transformed cube is no longer a single crystal but is disintegrated into individual c-In{sub 2}O{sub 3} domains with the size of about 5-10 nm. The induction time of approximately 15 s is estimated from the time-resolved Fourier transforms. The volume fraction of the transformed phase (c-In{sub 2}O{sub 3}), calculated from the shrinkage of the parent c-In(OH){sub 3} crystal in the recorded HR-TEM images, is used as a measure of the kinetics of c-In{sub 2}O{sub 3} crystallization within the framework of Avrami-Erofeev formalism. The Avrami exponent of {approx}3 is characteristic for a reaction mechanism with fast nucleation at the beginning of the reaction and subsequent three-dimensional growth of nuclei with a constant growth rate. The structural transformation path in reconstructive decomposition of c-In(OH){sub 3} to c-In{sub 2}O{sub 3} is discussed in terms of (i) the displacement of hydrogen atoms that lead to breaking the hydrogen bond between OH groups of [In(OH){sub 6}] octahedra and finally to their destabilization and (ii) transformation of the vertices-shared indium-oxygen octahedra in c-In(OH){sub 3} to vertices- and edge-shared octahedra in c-In{sub 2}O{sub 3}. - Graphical abstract: Frame-by-frame analysis of video sequences recorded of HR-TEM images reveals that a single cube-shaped In(OH){sub 3} nanocrystal with {l_brace}100{r_brace} morphology decomposes into bixbyite-type In{sub 2}O{sub 3} domains while being imaged. The mechanism of this decomposition is evaluated through the analysis of the structural relationship between initial (c-In(OH){sub 3}) and transformed (c-In{sub 2}O{sub 3}) phases and though the kinetics of the decomposition followed via the time-resolved shrinkage of the initial crystal of indium hydroxide. Highlights: Black-Right-Pointing-Pointer In-situ time-resolved High Resolution Transmission Electron Microscopy. Black-Right-Pointing-Pointer Crystallographic transformation path. Black-Right-Pointing-Pointer Kinetics of the decomposition in one nanocrystal.« less

Performance of the Wavelet Decomposition on Massively Parallel Architectures

NASA Technical Reports Server (NTRS)

El-Ghazawi, Tarek A.; LeMoigne, Jacqueline; Zukor, Dorothy (Technical Monitor)

2001-01-01

Traditionally, Fourier Transforms have been utilized for performing signal analysis and representation. But although it is straightforward to reconstruct a signal from its Fourier transform, no local description of the signal is included in its Fourier representation. To alleviate this problem, Windowed Fourier transforms and then wavelet transforms have been introduced, and it has been proven that wavelets give a better localization than traditional Fourier transforms, as well as a better division of the time- or space-frequency plane than Windowed Fourier transforms. Because of these properties and after the development of several fast algorithms for computing the wavelet representation of any signal, in particular the Multi-Resolution Analysis (MRA) developed by Mallat, wavelet transforms have increasingly been applied to signal analysis problems, especially real-life problems, in which speed is critical. In this paper we present and compare efficient wavelet decomposition algorithms on different parallel architectures. We report and analyze experimental measurements, using NASA remotely sensed images. Results show that our algorithms achieve significant performance gains on current high performance parallel systems, and meet scientific applications and multimedia requirements. The extensive performance measurements collected over a number of high-performance computer systems have revealed important architectural characteristics of these systems, in relation to the processing demands of the wavelet decomposition of digital images.

Wavelength-encoded tomography based on optical temporal Fourier transform

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhang, Chi; Wong, Kenneth K. Y., E-mail: kywong@eee.hku.hk

We propose and demonstrate a technique called wavelength-encoded tomography (WET) for non-invasive optical cross-sectional imaging, particularly beneficial in biological system. The WET utilizes time-lens to perform the optical Fourier transform, and the time-to-wavelength conversion generates a wavelength-encoded image of optical scattering from internal microstructures, analogous to the interferometery-based imaging such as optical coherence tomography. Optical Fourier transform, in principle, comes with twice as good axial resolution over the electrical Fourier transform, and will greatly simplify the digital signal processing after the data acquisition. As a proof-of-principle demonstration, a 150 -μm (ideally 36 μm) resolution is achieved based on a 7.5-nm bandwidth swept-pump,more » using a conventional optical spectrum analyzer. This approach can potentially achieve up to 100-MHz or even higher frame rate with some proven ultrafast spectrum analyzer. We believe that this technique is innovative towards the next-generation ultrafast optical tomographic imaging application.« less

Pulsed-High Field/High-Frequency EPR Spectroscopy

NASA Astrophysics Data System (ADS)

Fuhs, Michael; Moebius, Klaus

Pulsed high-field/high-frequency electron paramagnetic resonance (EPR) spectroscopy is used to disentangle many kinds of different effects often obscured in continuous wave (cw) EPR spectra at lower magnetic fields/microwave frequencies. While the high magnetic field increases the resolution of G tensors and of nuclear Larmor frequencies, the high frequencies allow for higher time resolution for molecular dynamics as well as for transient paramagnetic intermediates studied with time-resolved EPR. Pulsed EPR methods are used for example for relaxation-time studies, and pulsed Electron Nuclear DOuble Resonance (ENDOR) is used to resolve unresolved hyperfine structure hidden in inhomogeneous linewidths. In the present article we introduce the basic concepts and selected applications to structure and mobility studies on electron transfer systems, reaction centers of photosynthesis as well as biomimetic models. The article concludes with an introduction to stochastic EPR which makes use of an other concept for investigating resonance systems in order to increase the excitation bandwidth of pulsed EPR. The limited excitation bandwidth of pulses at high frequency is one of the main limitations which, so far, made Fourier transform methods hardly feasible.

Implementation of quantum and classical discrete fractional Fourier transforms.

PubMed

Weimann, Steffen; Perez-Leija, Armando; Lebugle, Maxime; Keil, Robert; Tichy, Malte; Gräfe, Markus; Heilmann, René; Nolte, Stefan; Moya-Cessa, Hector; Weihs, Gregor; Christodoulides, Demetrios N; Szameit, Alexander

2016-03-23

Fourier transforms, integer and fractional, are ubiquitous mathematical tools in basic and applied science. Certainly, since the ordinary Fourier transform is merely a particular case of a continuous set of fractional Fourier domains, every property and application of the ordinary Fourier transform becomes a special case of the fractional Fourier transform. Despite the great practical importance of the discrete Fourier transform, implementation of fractional orders of the corresponding discrete operation has been elusive. Here we report classical and quantum optical realizations of the discrete fractional Fourier transform. In the context of classical optics, we implement discrete fractional Fourier transforms of exemplary wave functions and experimentally demonstrate the shift theorem. Moreover, we apply this approach in the quantum realm to Fourier transform separable and path-entangled biphoton wave functions. The proposed approach is versatile and could find applications in various fields where Fourier transforms are essential tools.

Implementation of quantum and classical discrete fractional Fourier transforms

PubMed Central

Weimann, Steffen; Perez-Leija, Armando; Lebugle, Maxime; Keil, Robert; Tichy, Malte; Gräfe, Markus; Heilmann, René; Nolte, Stefan; Moya-Cessa, Hector; Weihs, Gregor; Christodoulides, Demetrios N.; Szameit, Alexander

2016-01-01

Fourier transforms, integer and fractional, are ubiquitous mathematical tools in basic and applied science. Certainly, since the ordinary Fourier transform is merely a particular case of a continuous set of fractional Fourier domains, every property and application of the ordinary Fourier transform becomes a special case of the fractional Fourier transform. Despite the great practical importance of the discrete Fourier transform, implementation of fractional orders of the corresponding discrete operation has been elusive. Here we report classical and quantum optical realizations of the discrete fractional Fourier transform. In the context of classical optics, we implement discrete fractional Fourier transforms of exemplary wave functions and experimentally demonstrate the shift theorem. Moreover, we apply this approach in the quantum realm to Fourier transform separable and path-entangled biphoton wave functions. The proposed approach is versatile and could find applications in various fields where Fourier transforms are essential tools. PMID:27006089

Accurate determination of the diffusion coefficient of proteins by Fourier analysis with whole column imaging detection.

PubMed

Zarabadi, Atefeh S; Pawliszyn, Janusz

2015-02-17

Analysis in the frequency domain is considered a powerful tool to elicit precise information from spectroscopic signals. In this study, the Fourier transformation technique is employed to determine the diffusion coefficient (D) of a number of proteins in the frequency domain. Analytical approaches are investigated for determination of D from both experimental and data treatment viewpoints. The diffusion process is modeled to calculate diffusion coefficients based on the Fourier transformation solution to Fick's law equation, and its results are compared to time domain results. The simulations characterize optimum spatial and temporal conditions and demonstrate the noise tolerance of the method. The proposed model is validated by its application for the electropherograms from the diffusion path of a set of proteins. Real-time dynamic scanning is conducted to monitor dispersion by employing whole column imaging detection technology in combination with capillary isoelectric focusing (CIEF) and the imaging plug flow (iPF) experiment. These experimental techniques provide different peak shapes, which are utilized to demonstrate the Fourier transformation ability in extracting diffusion coefficients out of irregular shape signals. Experimental results confirmed that the Fourier transformation procedure substantially enhanced the accuracy of the determined values compared to those obtained in the time domain.

Three dimensional rotating flow of Powell-Eyring nanofluid with non-Fourier's heat flux and non-Fick's mass flux theory

NASA Astrophysics Data System (ADS)

Ibrahim, Wubshet

2018-03-01

This article numerically examines three dimensional boundary layer flow of a rotating Powell-Eyring nanofluid. In modeling heat transfer processes, non-Fourier heat flux theory and for mass transfer non-Fick's mass flux theory are employed. This theory is recently re-initiated and it becomes the active research area to resolves some drawback associated with the famous Fourier heat flux and mass flux theory. The mathematical model of the flow problem is a system of non-linear partial differential equations which are obtained using the boundary layer analysis. The non-linear partial differential equations have been transformed into non-linear high order ordinary differential equations using similarity transformation. Employing bvp4c algorithm from matlab software routine, the numerical solution of the transformed ordinary differential equations is obtained. The governing equations are constrained by parameters such as rotation parameter λ , the non-Newtonian parameter N, dimensionless thermal relaxation and concentration relaxation parameters δt and δc . The impacts of these parameters have been discussed thoroughly and illustrated using graphs and tables. The findings show that thermal relaxation time δt reduces the thermal and concentration boundary layer thickness. Further, the results reveal that the rotational parameter λ has the effect of decreasing the velocity boundary layer thickness in both x and y directions. Further examination pinpoints that the skin friction coefficient along x-axis is an increasing and skin friction coefficient along y-axis is a decreasing function of rotation parameter λ . Furthermore, the non-Newtonian fluid parameter N has the characteristic of reducing the amount of local Nusselt numbers -f″ (0) and -g″ (0) both in x and y -directions.

Space-time domain solutions of the wave equation by a non-singular boundary integral method and Fourier transform.

PubMed

Klaseboer, Evert; Sepehrirahnama, Shahrokh; Chan, Derek Y C

2017-08-01

The general space-time evolution of the scattering of an incident acoustic plane wave pulse by an arbitrary configuration of targets is treated by employing a recently developed non-singular boundary integral method to solve the Helmholtz equation in the frequency domain from which the space-time solution of the wave equation is obtained using the fast Fourier transform. The non-singular boundary integral solution can enforce the radiation boundary condition at infinity exactly and can account for multiple scattering effects at all spacings between scatterers without adverse effects on the numerical precision. More generally, the absence of singular kernels in the non-singular integral equation confers high numerical stability and precision for smaller numbers of degrees of freedom. The use of fast Fourier transform to obtain the time dependence is not constrained to discrete time steps and is particularly efficient for studying the response to different incident pulses by the same configuration of scatterers. The precision that can be attained using a smaller number of Fourier components is also quantified.

Ultrafast and versatile spectroscopy by temporal Fourier transform

NASA Astrophysics Data System (ADS)

Zhang, Chi; Wei, Xiaoming; Marhic, Michel E.; Wong, Kenneth K. Y.

2014-06-01

One of the most remarkable and useful properties of a spatially converging lens system is its inherent ability to perform the Fourier transform; the same applies for the time-lens system. At the back focal plane of the time-lens, the spectral information can be instantaneously obtained in the time axis. By implementing temporal Fourier transform for spectroscopy applications, this time-lens-based architecture can provide orders of magnitude improvement over the state-of-art spatial-dispersion-based spectroscopy in terms of the frame rate. On the other hand, in addition to the single-lens structure, the multi-lens structures (e.g. telescope or wide-angle scope) will provide very versatile operating conditions. Leveraging the merit of instantaneous response, as well as the flexible lens structure, here we present a 100-MHz frame rate spectroscopy system - the parametric spectro-temporal analyzer (PASTA), which achieves 17 times zoom in/out ratio for different observation ranges.

TH-E-17A-01: Internal Respiratory Surrogate for 4D CT Using Fourier Transform and Anatomical Features

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hui, C; Suh, Y; Robertson, D

Purpose: To develop a novel algorithm to generate internal respiratory signals for sorting of four-dimensional (4D) computed tomography (CT) images. Methods: The proposed algorithm extracted multiple time resolved features as potential respiratory signals. These features were taken from the 4D CT images and its Fourier transformed space. Several low-frequency locations in the Fourier space and selected anatomical features from the images were used as potential respiratory signals. A clustering algorithm was then used to search for the group of appropriate potential respiratory signals. The chosen signals were then normalized and averaged to form the final internal respiratory signal. Performance ofmore » the algorithm was tested in 50 4D CT data sets and results were compared with external signals from the real-time position management (RPM) system. Results: In almost all cases, the proposed algorithm generated internal respiratory signals that visibly matched the external respiratory signals from the RPM system. On average, the end inspiration times calculated by the proposed algorithm were within 0.1 s of those given by the RPM system. Less than 3% of the calculated end inspiration times were more than one time frame away from those given by the RPM system. In 3 out of the 50 cases, the proposed algorithm generated internal respiratory signals that were significantly smoother than the RPM signals. In these cases, images sorted using the internal respiratory signals showed fewer artifacts in locations corresponding to the discrepancy in the internal and external respiratory signals. Conclusion: We developed a robust algorithm that generates internal respiratory signals from 4D CT images. In some cases, it even showed the potential to outperform the RPM system. The proposed algorithm is completely automatic and generally takes less than 2 min to process. It can be easily implemented into the clinic and can potentially replace the use of external surrogates.« less

Deconvolution of Stark broadened spectra for multi-point density measurements in a flow Z-pinch

DOE PAGES

Vogman, G. V.; Shumlak, U.

2011-10-13

Stark broadened emission spectra, once separated from other broadening effects, provide a convenient non-perturbing means of making plasma density measurements. A deconvolution technique has been developed to measure plasma densities in the ZaP flow Z-pinch experiment. The ZaP experiment uses sheared flow to mitigate MHD instabilities. The pinches exhibit Stark broadened emission spectra, which are captured at 20 locations using a multi-chord spectroscopic system. Spectra that are time- and chord-integrated are well approximated by a Voigt function. The proposed method simultaneously resolves plasma electron density and ion temperature by deconvolving the spectral Voigt profile into constituent functions: a Gaussian functionmore » associated with instrument effects and Doppler broadening by temperature; and a Lorentzian function associated with Stark broadening by electron density. The method uses analytic Fourier transforms of the constituent functions to fit the Voigt profile in the Fourier domain. The method is discussed and compared to a basic least-squares fit. The Fourier transform fitting routine requires fewer fitting parameters and shows promise in being less susceptible to instrumental noise and to contamination from neighboring spectral lines. The method is evaluated and tested using simulated lines and is applied to experimental data for the 229.69 nm C III line from multiple chords to determine plasma density and temperature across the diameter of the pinch. As a result, these measurements are used to gain a better understanding of Z-pinch equilibria.« less

Deconvolution of Stark broadened spectra for multi-point density measurements in a flow Z-pinch

DOE Office of Scientific and Technical Information (OSTI.GOV)

Vogman, G. V.; Shumlak, U.

2011-10-15

Stark broadened emission spectra, once separated from other broadening effects, provide a convenient non-perturbing means of making plasma density measurements. A deconvolution technique has been developed to measure plasma densities in the ZaP flow Z-pinch experiment. The ZaP experiment uses sheared flow to mitigate MHD instabilities. The pinches exhibit Stark broadened emission spectra, which are captured at 20 locations using a multi-chord spectroscopic system. Spectra that are time- and chord-integrated are well approximated by a Voigt function. The proposed method simultaneously resolves plasma electron density and ion temperature by deconvolving the spectral Voigt profile into constituent functions: a Gaussian functionmore » associated with instrument effects and Doppler broadening by temperature; and a Lorentzian function associated with Stark broadening by electron density. The method uses analytic Fourier transforms of the constituent functions to fit the Voigt profile in the Fourier domain. The method is discussed and compared to a basic least-squares fit. The Fourier transform fitting routine requires fewer fitting parameters and shows promise in being less susceptible to instrumental noise and to contamination from neighboring spectral lines. The method is evaluated and tested using simulated lines and is applied to experimental data for the 229.69 nm C III line from multiple chords to determine plasma density and temperature across the diameter of the pinch. These measurements are used to gain a better understanding of Z-pinch equilibria.« less

Noninterferometric Two-Dimensional Fourier-Transform Spectroscopy of Multilevel Systems

NASA Astrophysics Data System (ADS)

Davis, J. A.; Dao, L. V.; Do, M. T.; Hannaford, P.; Nugent, K. A.; Quiney, H. M.

2008-06-01

We demonstrate a technique that determines the phase of the photon-echo emission from spectrally resolved intensity data without requiring phase-stabilized input pulses. The full complex polarization of the emission is determined from spectral intensity measurements. The validity of this technique is demonstrated using simulated data, and is then applied to the analysis of two-color data obtained from the light-harvesting molecule lycopene.

A Unified Method of Finding Laplace Transforms, Fourier Transforms, and Fourier Series. [and] An Inversion Method for Laplace Transforms, Fourier Transforms, and Fourier Series. Integral Transforms and Series Expansions. Modules and Monographs in Undergraduate Mathematics and Its Applications Project. UMAP Units 324 and 325.

ERIC Educational Resources Information Center

Grimm, C. A.

This document contains two units that examine integral transforms and series expansions. In the first module, the user is expected to learn how to use the unified method presented to obtain Laplace transforms, Fourier transforms, complex Fourier series, real Fourier series, and half-range sine series for given piecewise continuous functions. In…

[The investigation and simulation of a novel spatially modulated micro-Fourier transform spectrometer].

PubMed

Kong, Yan-mei; Liang, Jing-qiu; Wang, Bo; Liang, Zhong-zhu; Xu, Da-wei; Zhang, Jun

2009-04-01

Fourier transform spectrometer (FTS) is widely used in science and industry for the measurement of electromagnetic spectra, and it's trend of minimization is particularly pronounced in many applications. A novel model of a micro FTS with no moving parts is proposed and analyzed. During the analysis, the gradients which mainly introduce the phase error are accounted for in details. Based on these assumptions and the improved Mertz phase correcting method, the spectrum of the signal is simulated, given the real extended light source. The resolution can reach 3.43 nm@800 nm, with high SNR limiting resolving ability 6.8 dB. The novel micro FTS could be made by MOEMS technology, which has some advantages over the conventional micro dispersive spectrometers based on the traditional technology, and this method can also afford some new concepts on the design of spectrometers. The research work is underway to demonstrate the theory.

Characterization of plasmonic hole arrays as transparent electrical contacts for organic photovoltaics using high-brightness Fourier transform methods

DOE PAGES

Camino, Fernando E.; Nam, Chang-Yong; Pang, Yutong T.; ...

2014-05-15

Here we present a methodology for probing light-matter interactions in prototype photovoltaic devices consisting of an organic semiconductor active layer with a semitransparent metal electrical contact exhibiting surface plasmon-based enhanced optical transmission. We achieve high-spectral irradiance in a spot size of less than 100 μm using a high-brightness laser-driven light source and appropriate coupling optics. Spatially resolved Fourier transform photocurrent spectroscopy in the visible and near-infrared spectral regions allows us to measure external quantum efficiency with high sensitivity in small-area devices (<1 mm 2). Lastly, this allows for rapid fabrication of variable-pitch sub-wavelength hole arrays in metal films for usemore » as transparent electrical contacts, and evaluation of the evanescent and propagating mode coupling to resonances in the active layer.« less

Application of point-to-point matching algorithms for background correction in on-line liquid chromatography-Fourier transform infrared spectrometry (LC-FTIR).

PubMed

Kuligowski, J; Quintás, G; Garrigues, S; de la Guardia, M

2010-03-15

A new background correction method for the on-line coupling of gradient liquid chromatography and Fourier transform infrared spectrometry has been developed. It is based on the use of a point-to-point matching algorithm that compares the absorption spectra of the sample data set with those of a previously recorded reference data set in order to select an appropriate reference spectrum. The spectral range used for the point-to-point comparison is selected with minimal user-interaction, thus facilitating considerably the application of the whole method. The background correction method has been successfully tested on a chromatographic separation of four nitrophenols running acetonitrile (0.08%, v/v TFA):water (0.08%, v/v TFA) gradients with compositions ranging from 35 to 85% (v/v) acetonitrile, giving accurate results for both, baseline resolved and overlapped peaks. Copyright (c) 2009 Elsevier B.V. All rights reserved.

Fourier transform microwave spectroscopy of the SiCl+ ion

NASA Astrophysics Data System (ADS)

Tanaka, Keiichi; Harada, Kensuke; Cabezas, Carlos; Endo, Yasuki

2018-03-01

Fourier transform microwave spectra for the J = 1 ← 0 and 2 ← 1 rotational transitions of the SiCl+ ion were observed for two isotopologues (35 Cl and 37 Cl) in the ground and the first excited vibrational states of the ground 1Σ+ electronic state. Thanks to the high resolution of the FTMW spectrometer, hyperfine structures due to the quadrupole moment of the chlorine nucleus and the nuclear spin-rotation interaction were fully resolved. The observed FTMW spectra were combined with previously reported MMW and diode laser spectra in an analysis to determine the mass-independent Dunham coefficients Uk,l as well as a mass scaling parameter Δ01Cl = - 0.856 (30) . The equilibrium bond length of SiCl+ determined is re = 1.9439729 (10) Å and the nuclear quadrupole coupling constant of Si35 Cl+ is eQqe = - 11.8788 (23) MHz.

Artefacts in geometric phase analysis of compound materials.

PubMed

Peters, Jonathan J P; Beanland, Richard; Alexe, Marin; Cockburn, John W; Revin, Dmitry G; Zhang, Shiyong Y; Sanchez, Ana M

2015-10-01

The geometric phase analysis (GPA) algorithm is known as a robust and straightforward technique that can be used to measure lattice strains in high resolution transmission electron microscope (TEM) images. It is also attractive for analysis of aberration-corrected scanning TEM (ac-STEM) images that resolve every atom column, since it uses Fourier transforms and does not require real-space peak detection and assignment to appropriate sublattices. Here it is demonstrated that, in ac-STEM images of compound materials with compositionally distinct atom columns, an additional geometric phase is present in the Fourier transform. If the structure changes from one area to another in the image (e.g. across an interface), the change in this additional phase will appear as a strain in conventional GPA, even if there is no lattice strain. Strategies to avoid this pitfall are outlined. Copyright © 2015 Elsevier B.V. All rights reserved.

Ground cross-modal impedance as a tool for analyzing ground/plate interaction and ground wave propagation.

PubMed

Grau, L; Laulagnet, B

2015-05-01

An analytical approach is investigated to model ground-plate interaction based on modal decomposition and the two-dimensional Fourier transform. A finite rectangular plate subjected to flexural vibration is coupled with the ground and modeled with the Kirchhoff hypothesis. A Navier equation represents the stratified ground, assumed infinite in the x- and y-directions and free at the top surface. To obtain an analytical solution, modal decomposition is applied to the structure and a Fourier Transform is applied to the ground. The result is a new tool for analyzing ground-plate interaction to resolve this problem: ground cross-modal impedance. It allows quantifying the added-stiffness, added-mass, and added-damping from the ground to the structure. Similarity with the parallel acoustic problem is highlighted. A comparison between the theory and the experiment shows good matching. Finally, specific cases are investigated, notably the influence of layer depth on plate vibration.

Definition of a metrology servo-system for a solar imaging fourier transform spectrometer working in the far UV (IFTSUV)

NASA Astrophysics Data System (ADS)

Ruiz de Galarreta Fanju, C.; Philippon, A.; Bouzit, M.; Appourchaux, T.; Vial, J.-C.; Maillard, J.-P.; Lemaire, P.

2017-11-01

The understanding of the solar outer atmosphere requires a simultaneous combination of imaging and spectral observations concerning the far UV lines that arise from the high chromospheres up to the corona. These observations must be performed with enough spectral, spatial and temporal resolution to reveal the small atmospheric structures and to resolve the solar dynamics. An Imaging Fourier Transform Spectrometer working in the far-UV (IFTSUV, Figure 1) is an attractive instrumental solution to fulfill these requirements. However, due to the short wavelength, to preserve IFTSUV spectral precision and Signal to Noise Ratio (SNR) requires a high optical surface quality and a very accurate (linear and angular) metrology to maintain the optical path difference (OPD) during the entire scanning process by: optical path difference sampling trigger; and dynamic alignment for tip/tilt compensation (Figure 2).

High-resolution Fourier transform infrared synchrotron spectroscopy of the NO2 in-plane rock band of nitromethane

NASA Astrophysics Data System (ADS)

Dawadi, Mahesh B.; Twagirayezu, Sylvestre; Perry, David S.; Billinghurst, Brant E.

2015-09-01

The high-resolution rotationally resolved Fourier-transform infrared spectrum of the NO2 in-plane rock band (440-510 cm-1) of nitromethane (CH3NO2) has been recorded using the Far-Infrared Beamline at the Canadian Light Source, with a resolution of 0.00096 cm-1. About 1773 transitions reaching the upper state levels m‧ = 0; Ka‧ ⩽ 7;J‧ ⩽ 50 have been assigned using an automated ground-state combination difference program together with the traditional Loomis-Wood approach. These data from the lowest torsional state, m‧ = 0, were fit using the six-fold torsion-rotation program developed by Ilyushin et al. (2010). The analysis reveals that the rotational energy level structure in the upper vibrational state is similar to that of the ground vibrational state, but the sign and magnitude of high-order constants are significantly changed suggesting the presence of multiple perturbations.

Time-resolved diffusion tomographic 2D and 3D imaging in highly scattering turbid media

NASA Technical Reports Server (NTRS)

Alfano, Robert R. (Inventor); Cai, Wei (Inventor); Liu, Feng (Inventor); Lax, Melvin (Inventor); Das, Bidyut B. (Inventor)

1999-01-01

A method for imaging objects in highly scattering turbid media. According to one embodiment of the invention, the method involves using a plurality of intersecting source/detectors sets and time-resolving equipment to generate a plurality of time-resolved intensity curves for the diffusive component of light emergent from the medium. For each of the curves, the intensities at a plurality of times are then inputted into the following inverse reconstruction algorithm to form an image of the medium: ##EQU1## wherein W is a matrix relating output at source and detector positions r.sub.s and r.sub.d, at time t, to position r, .LAMBDA. is a regularization matrix, chosen for convenience to be diagonal, but selected in a way related to the ratio of the noise, to fluctuations in the absorption (or diffusion) X.sub.j that we are trying to determine: .LAMBDA..sub.ij =.lambda..sub.j .delta..sub.ij with .lambda..sub.j =/<.DELTA.Xj.DELTA.Xj> Y is the data collected at the detectors, and X.sup.k is the kth iterate toward the desired absoption information. An algorithm, which combines a two dimensional (2D) matrix inversion with a one-dimensional (1D) Fourier transform inversion is used to obtain images of three dimensional hidden objects in turbid scattering media.

Time-resolved diffusion tomographic 2D and 3D imaging in highly scattering turbid media

NASA Technical Reports Server (NTRS)

Alfano, Robert R. (Inventor); Cai, Wei (Inventor); Gayen, Swapan K. (Inventor)

2000-01-01

A method for imaging objects in highly scattering turbid media. According to one embodiment of the invention, the method involves using a plurality of intersecting source/detectors sets and time-resolving equipment to generate a plurality of time-resolved intensity curves for the diffusive component of light emergent from the medium. For each of the curves, the intensities at a plurality of times are then inputted into the following inverse reconstruction algorithm to form an image of the medium: wherein W is a matrix relating output at source and detector positions r.sub.s and r.sub.d, at time t, to position r, .LAMBDA. is a regularization matrix, chosen for convenience to be diagonal, but selected in a way related to the ratio of the noise, to fluctuations in the absorption (or diffusion) X.sub.j that we are trying to determine: .LAMBDA..sub.ij =.lambda..sub.j .delta..sub.ij with .lambda..sub.j =/<.DELTA.Xj.DELTA.Xj> Y is the data collected at the detectors, and X.sup.k is the kth iterate toward the desired absorption information. An algorithm, which combines a two dimensional (2D) matrix inversion with a one-dimensional (1D) Fourier transform inversion is used to obtain images of three dimensional hidden objects in turbid scattering media.

Discrimination of dipicolinic acid and its interferents by femtosecond coherent Raman spectroscopy

NASA Astrophysics Data System (ADS)

Huang, Yu; Dogariu, Arthur; Avitzour, Yoav; Murawski, Robert K.; Pestov, Dmitry; Zhi, Miaochan; Sokolov, Alexei V.; Scully, Marlan O.

2006-12-01

Measurements of the beat frequencies between vibrational modes of dipicolinic acid (DPA) and a series of other molecules (interferents) are presented. The results were obtained from femtosecond time-resolved coherent Raman scattering, and the vibrational level spacings were determined from a Fourier transform of the signal versus probe pulse delay. The entire spectrum of the generated signal is recorded in order to demonstrate multimode excitation and to explain the variety of qualitatively different traces that can be obtained for the same molecule. Since the spectral signature of DPA is unique enough to be used for identification purposes, this technique has the potential to detect hazardous bacterial species, such as anthrax spores.

Studies in astronomical time series analysis. III - Fourier transforms, autocorrelation functions, and cross-correlation functions of unevenly spaced data

NASA Technical Reports Server (NTRS)

Scargle, Jeffrey D.

1989-01-01

This paper develops techniques to evaluate the discrete Fourier transform (DFT), the autocorrelation function (ACF), and the cross-correlation function (CCF) of time series which are not evenly sampled. The series may consist of quantized point data (e.g., yes/no processes such as photon arrival). The DFT, which can be inverted to recover the original data and the sampling, is used to compute correlation functions by means of a procedure which is effectively, but not explicitly, an interpolation. The CCF can be computed for two time series not even sampled at the same set of times. Techniques for removing the distortion of the correlation functions caused by the sampling, determining the value of a constant component to the data, and treating unequally weighted data are also discussed. FORTRAN code for the Fourier transform algorithm and numerical examples of the techniques are given.

A new approach for measuring power spectra and reconstructing time series in active galactic nuclei

NASA Astrophysics Data System (ADS)

Li, Yan-Rong; Wang, Jian-Min

2018-05-01

We provide a new approach to measure power spectra and reconstruct time series in active galactic nuclei (AGNs) based on the fact that the Fourier transform of AGN stochastic variations is a series of complex Gaussian random variables. The approach parametrizes a stochastic series in frequency domain and transforms it back to time domain to fit the observed data. The parameters and their uncertainties are derived in a Bayesian framework, which also allows us to compare the relative merits of different power spectral density models. The well-developed fast Fourier transform algorithm together with parallel computation enables an acceptable time complexity for the approach.

Indium hydroxide to oxide decomposition observed in one nanocrystal during in situ transmission electron microscopy studies

NASA Astrophysics Data System (ADS)

Miehe, Gerhard; Lauterbach, Stefan; Kleebe, Hans-Joachim; Gurlo, Aleksander

2013-02-01

The high-resolution transmission electron microscopy (HR-TEM) is used to study, in situ, spatially resolved decomposition in individual nanocrystals of metal hydroxides and oxyhydroxides. This case study reports on the decomposition of indium hydroxide (c-In(OH)3) to bixbyite-type indium oxide (c-In2O3). The electron beam is focused onto a single cube-shaped In(OH)3 crystal of {100} morphology with ca. 35 nm edge length and a sequence of HR-TEM images was recorded during electron beam irradiation. The frame-by-frame analysis of video sequences allows for the in situ, time-resolved observation of the shape and orientation of the transformed crystals, which in turn enables the evaluation of the kinetics of c-In2O3 crystallization. Supplementary material (video of the transformation) related to this article can be found online at 10.1016/j.jssc.2012.09.022. After irradiation the shape of the parent cube-shaped crystal is preserved, however, its linear dimension (edge) is reduced by the factor 1.20. The corresponding spotted selected area electron diffraction (SAED) pattern representing zone [001] of c-In(OH)3 is transformed to a diffuse strongly textured ring-like pattern of c-In2O3 that indicates the transformed cube is no longer a single crystal but is disintegrated into individual c-In2O3 domains with the size of about 5-10 nm. The induction time of approximately 15 s is estimated from the time-resolved Fourier transforms. The volume fraction of the transformed phase (c-In2O3), calculated from the shrinkage of the parent c-In(OH)3 crystal in the recorded HR-TEM images, is used as a measure of the kinetics of c-In2O3 crystallization within the framework of Avrami-Erofeev formalism. The Avrami exponent of ˜3 is characteristic for a reaction mechanism with fast nucleation at the beginning of the reaction and subsequent three-dimensional growth of nuclei with a constant growth rate. The structural transformation path in reconstructive decomposition of c-In(OH)3 to c-In2O3 is discussed in terms of (i) the displacement of hydrogen atoms that lead to breaking the hydrogen bond between OH groups of [In(OH)6] octahedra and finally to their destabilization and (ii) transformation of the vertices-shared indium-oxygen octahedra in c-In(OH)3 to vertices- and edge-shared octahedra in c-In2O3.

Time-frequency representation of autoionization dynamics in helium

NASA Astrophysics Data System (ADS)

Busto, D.; Barreau, L.; Isinger, M.; Turconi, M.; Alexandridi, C.; Harth, A.; Zhong, S.; Squibb, R. J.; Kroon, D.; Plogmaker, S.; Miranda, M.; Jiménez-Galán, Á.; Argenti, L.; Arnold, C. L.; Feifel, R.; Martín, F.; Gisselbrecht, M.; L'Huillier, A.; Salières, P.

2018-02-01

Autoionization, which results from the interference between direct photoionization and photoexcitation to a discrete state decaying to the continuum by configuration interaction, is a well known example of the important role of electron correlation in light-matter interaction. Information on this process can be obtained by studying the spectral, or equivalently, temporal complex amplitude of the ionized electron wave packet. Using an energy-resolved interferometric technique, we measure the spectral amplitude and phase of autoionized wave packets emitted via the sp2+ and sp3+ resonances in helium. These measurements allow us to reconstruct the corresponding temporal profiles by Fourier transform. In addition, applying various time-frequency representations, we observe the build-up of the wave packets in the continuum, monitor the instantaneous frequencies emitted at any time and disentangle the dynamics of the direct and resonant ionization channels.

Counting individual sulfur atoms in a protein by ultrahighresolution Fourier transform ion cyclotron resonance mass spectrometry: Experimental resolution of isotopic fine structure in proteins

PubMed Central

Shi, Stone D.-H.; Hendrickson, Christopher L.; Marshall, Alan G.

1998-01-01

A typical molecular ion mass spectrum consists of a sum of signals from species of various possible isotopic compositions. Only the monoisotopic peak (e.g., all carbons are 12C; all nitrogens are 14N, etc.) has a unique elemental composition. Every other isotope peak at approximately integer multiples of ∼1 Da higher in nominal mass represents a sum of contributions from isotope combinations differing by a few mDa (e.g., two 13C vs. two 15N vs. one 13C and one 15N vs. 34S, vs. 18O, etc., at ∼2 Da higher in mass than the monoisotopic mass). At sufficiently high mass resolving power, each of these nominal-mass peaks resolves into its isotopic fine structure. Here, we report resolution of the isotopic fine structure of proteins up to 15.8 kDa (isotopic 13C,15N doubly depleted tumor suppressor protein, p16), made possible by electrospray ionization followed by ultrahigh-resolution Fourier transform ion cyclotron resonance mass analysis at 9.4 tesla. Further, a resolving power of m/Δm50% ≈8,000,000 has been achieved on bovine ubiquitin (8.6 kDa). These results represent a 10-fold increase in the highest mass at which isotopic fine structure previously had been observed. Finally, because isotopic fine structure reveals elemental composition directly, it can be used to confirm or determine molecular formula. For p16, for example, we were able to determine (5.1 ± 0.3) the correct number (five) of sulfur atoms solely from the abundance ratio of the resolved 34S peak to the monoisotopic peak. PMID:9751700

Industrial realization of a direct Fourier transform in automated experimental data processing systems

NASA Technical Reports Server (NTRS)

Lyubashevskiy, G. S.

1973-01-01

Fourier processing of automatic signals transforms direct current voltage into a numerical form through bandpass filtration in time-pulse multiplying devices. It is shown that the ratio of the interference energy to the useful signal energy is inversely proportional to the square of the product of the depth of the width modulation and the ratio of the time constant averaging to the cross-multiplied signals.

Beyond MOS and fibers: Optical Fourier-transform Imaging Unit for Cananea Observatory (OFIUCO)

NASA Astrophysics Data System (ADS)

Nieto-Suárez, M. A.; Rosales-Ortega, F. F.; Castillo, E.; García, P.; Escobedo, G.; Sánchez, S. F.; González, J.; Iglesias-Páramo, J.; Mollá, M.; Chávez, M.; Bertone, E.; et al.

2017-11-01

Many physical processes in astronomy are still hampered by the lack of spatial and spectral resolution, and also restricted to the field-of-view (FoV) of current 2D spectroscopy instruments available worldwide. It is due to that, many of the ongoing or proposed studies are based on large-scale imaging and/or spectroscopic surveys. Under this philosophy, large aperture telescopes are dedicated to the study of intrinsically faint and/or distance objects, covering small FoVs, with high spatial resolution, while smaller telescopes are devoted to wide-field explorations. However, future astronomical surveys, should be addressed by acquiring un-biases, spatially resolved, high-quality spectroscopic information for a wide FoV. Therefore, and in order to improve the current instrumental offer in the Observatorio Astrofísico Guillermo Haro (OAGH) in Cananea, Mexico (INAOE); and to explore a possible instrument for the future Telescopio San Pedro Mártir (6.5m), we are currently integrating at INAOE an instrument prototype that will provide us with un-biased wide-field (few arcmin) spectroscopic information, and with the flexibility of operating at different spectral resolutions (R 1-20000), with a spatial resolution limited by seeing, and therefore, to be used in a wide range of astronomical problems. This instrument called OFIUCO: Optical Fourier-transform Imaging Unit for Cananea Observatory, will make use of the Fourier Transform Spectroscopic technique, which has been proved to be feasible in the optical wavelength range (350-1000 nm) with designs such as SITELLE (CFHT). We describe here the basic technical description of a Fourier transform spectrograph with important modifications from previous astronomical versions, as well as the technical advantages and weakness, and the science cases in which this instrument can be implemented.

PLANE-INTEGRATED OPEN-PATH FOURIER TRANSFORM INFRARED SPECTROMETRY METHODOLOGY FOR ANAEROBIC SWINE LAGOON EMISSION MEASUREMENTS

EPA Science Inventory

Emissions of ammonia and methane from an anaerobic lagoon at a swine animal feeding operation were evaluated five times over a period of two years. The plane-integrated (PI) open-path Fourier transform infrared spectrometry (OP-FTIR) methodology was used to transect the plume at ...

Infrared absorption of CH3OSO detected with time-resolved Fourier-transform spectroscopy.

PubMed

Chen, Jin-Dah; Lee, Yuan-Pern

2011-03-07

A step-scan Fourier-transform spectrometer coupled with a multipass absorption cell was employed to detect temporally resolved infrared absorption spectra of CH(3)OSO produced upon irradiation of a flowing gaseous mixture of CH(3)OS(O)Cl in N(2) or CO(2) at 248 nm. Two intense transient features with origins near 1152 and 994 cm(-1) are assigned to syn-CH(3)OSO; the former is attributed to overlapping bands at 1154 ± 3 and 1151 ± 3 cm(-1), assigned to the S=O stretching mixed with CH(3) rocking (ν(8)) and the S=O stretching mixed with CH(3) wagging (ν(9)) modes, respectively, and the latter to the C-O stretching (ν(10)) mode at 994 ± 6 cm(-1). Two weak bands at 2991 ± 6 and 2956 ± 3 cm(-1) are assigned as the CH(3) antisymmetric stretching (ν(2)) and symmetric stretching (ν(3)) modes, respectively. Observed vibrational transition wavenumbers agree satisfactorily with those predicted with quantum-chemical calculations at level B3P86∕aug-cc-pVTZ. Based on rotational parameters predicted at that level, the simulated rotational contours of these bands agree satisfactorily with experimental results. The simulation indicates that the S=O stretching mode of anti-CH(3)OSO near 1164 cm(-1) likely makes a small contribution to the observed band near 1152 cm(-1). A simple kinetic model of self-reaction is employed to account for the decay of CH(3)OSO and yields a second-order rate coefficient k=(4 ± 2)×10(-10) cm(3)molecule(-1)s(-1). © 2011 American Institute of Physics.

First Signal on the Cryogenic Fourier-Transform Ion Cyclotron Resonance Mass Spectrometer

PubMed Central

Lin, Cheng; Mathur, Raman; Aizikov, Kostantin; O'Connor, Peter B.

2009-01-01

The construction and achievement of the first signal on a cryogenic Fourier-transform ion cyclotron resonance mass spectrometer (FT-ICR-MS) are reported here, demonstrating proof-of-concept of this new instrument design. Building the FTICR cell into the cold bore of a superconducting magnet provided advantages over conventional warm bore design. At 4.2 K, the vacuum system cryopumps itself, thus removing the requirement for a large bore to achieve the desired pumping speed for maintaining base pressure. Furthermore, because the bore diameter has been reduced, the amount of magnet wire needed to achieve high field and homogeneity was also reduced, greatly decreasing the cost/Tesla of the magnet. The current instrument implements an actively shielded 14-Tesla magnet of vertical design with an external matrix assisted laser desorption/ionization (MALDI) source. The first signal was obtained by detecting the laser desorbed/ionized (LDI) C60+• ions, with the magnet at 7 Tesla, unshimmed, and the preamplifier mounted outside of the vacuum chamber at room temperature. A subsequent experiment done with the magnet at 14 Tesla and properly shimmed produced a C60 spectrum showing ∼350,000 resolving power at m/z ∼720. Increased magnetic field strength improves many FTMS performance parameters simultaneously, particularly mass resolving power and accuracy. PMID:17931882

a Signal-Tuned Gabor Transform with Application to Eeg Analysis

NASA Astrophysics Data System (ADS)

Torreão, José R. A.; Victer, Silvia M. C.; Fernandes, João L.

2013-04-01

We introduce a time-frequency transform based on Gabor functions whose parameters are given by the Fourier transform of the analyzed signal. At any given frequency, the width and the phase of the Gabor function are obtained, respectively, from the magnitude and the phase of the signal's corresponding Fourier component, yielding an analyzing kernel which is a representation of the signal's content at that particular frequency. The resulting Gabor transform tunes itself to the input signal, allowing the accurate detection of time and frequency events, even in situations where the traditional Gabor and S-transform approaches tend to fail. This is the case, for instance, when considering the time-frequency representation of electroencephalogram traces (EEG) of epileptic subjects, as illustrated by the experimental study presented here.

Use of Fourier transforms for asynoptic mapping: Applications to the Upper Atmosphere Research Satellite microwave limb sounder

NASA Technical Reports Server (NTRS)

Elson, Lee S.; Froidevaux, Lucien

1993-01-01

Fourier analysis has been applied to data obtained from limb viewing instruments on the Upper Atmosphere Research Satellite. A coordinate system rotation facilitates the efficient computation of Fourier transforms in the temporal and longitudinal domains. Fields such as ozone (O3), chlorine monoxide (ClO), temperature, and water vapor have been transformed by this process. The transforms have been inverted to provide maps of these quantities at selected times, providing a method of accurate time interpolation. Maps obtained by this process show evidence of both horizontal and vertical transport of important trace species such as O3 and ClO. An examination of the polar regions indicates that large-scale planetary variations are likely to play a significant role in transporting midstratospheric O3 into the polar regions. There is also evidence that downward transport occurs, providing a means of moving O3 into the polar vortex at lower altitudes. The transforms themselves show the structure and propagation characteristics of wave variations.

A Method to Compute the Force Signature of a Body Impacting on a Linear Elastic Structure Using Fourier Analysis

DTIC Science & Technology

1982-09-17

FK * 1PK (2) The convolution of two transforms in time domain is the inverse transform of the product in frequency domain. Thus Rp(s) - Fgc() Ipg(*) (3...its inverse transform by: R,(r)- R,(a.)e’’ do. (5)2w In order to nuke use f a very accurate numerical method to ompute Fourier "ke and coil...taorm. When the inverse transform it tken by using Eq. (15), the cosine transform, because it converges faster than the sine transform refu-ft the

Discrete Fourier Transform Analysis in a Complex Vector Space

NASA Technical Reports Server (NTRS)

Dean, Bruce H.

2009-01-01

Alternative computational strategies for the Discrete Fourier Transform (DFT) have been developed using analysis of geometric manifolds. This approach provides a general framework for performing DFT calculations, and suggests a more efficient implementation of the DFT for applications using iterative transform methods, particularly phase retrieval. The DFT can thus be implemented using fewer operations when compared to the usual DFT counterpart. The software decreases the run time of the DFT in certain applications such as phase retrieval that iteratively call the DFT function. The algorithm exploits a special computational approach based on analysis of the DFT as a transformation in a complex vector space. As such, this approach has the potential to realize a DFT computation that approaches N operations versus Nlog(N) operations for the equivalent Fast Fourier Transform (FFT) calculation.

Time-Resolved Chemical Mapping in Light-Emitting Electrochemical Cells.

PubMed

Jafari, Mohammad Javad; Liu, Jiang; Engquist, Isak; Ederth, Thomas

2017-01-25

An understanding of the doping and ion distributions in light-emitting electrochemical cells (LECs) is required to approach a realistic conduction model which can precisely explain the electrochemical reactions, p-n junction formation, and ion dynamics in the active layer and to provide relevant information about LECs for systematic improvement of function and manufacture. Here, Fourier-transform infrared (FTIR) microscopy is used to monitor anion density profile and polymer structure in situ and for time-resolved mapping of electrochemical doping in an LEC under bias. The results are in very good agreement with the electrochemical doping model with respect to ion redistribution and formation of a dynamic p-n junction in the active layer. We also physically slow ions by decreasing the working temperature and study frozen-junction formation and immobilization of ions in a fixed-junction LEC device by FTIR imaging. The obtained results show irreversibility of the ion redistribution and polymer doping in a fixed-junction device. In addition, we demonstrate that infrared microscopy is a useful tool for in situ characterization of electroactive organic materials.

Real-Time Fourier Transformed Holographic Associative Memory With Photorefractive Material

NASA Astrophysics Data System (ADS)

Changsuk, Oh; Hankyu, Park

1989-02-01

We describe a volume holographic associative memory using photorefractive material and conventional planar mirror. Multiple hologram is generated with two angular multiplexed writing beams and Fourier transformed object beam in BaTiO3 crystal at 0.6328 μm. Complete image can be recalled successfully by partial input of original stored image. It is proved that our system is useful for optical implementation of real-time associative memory and location addressable memory.

Delineation of First-Order Elastic Property Closures for Hexagonal Metals Using Fast Fourier Transforms

PubMed Central

Landry, Nicholas W.; Knezevic, Marko

2015-01-01

Property closures are envelopes representing the complete set of theoretically feasible macroscopic property combinations for a given material system. In this paper, we present a computational procedure based on fast Fourier transforms (FFTs) for delineation of elastic property closures for hexagonal close packed (HCP) metals. The procedure consists of building a database of non-zero Fourier transforms for each component of the elastic stiffness tensor, calculating the Fourier transforms of orientation distribution functions (ODFs), and calculating the ODF-to-elastic property bounds in the Fourier space. In earlier studies, HCP closures were computed using the generalized spherical harmonics (GSH) representation and an assumption of orthotropic sample symmetry; here, the FFT approach allowed us to successfully calculate the closures for a range of HCP metals without invoking any sample symmetry assumption. The methodology presented here facilitates for the first time computation of property closures involving normal-shear coupling stiffness coefficients. We found that the representation of these property linkages using FFTs need more terms compared to GSH representations. However, the use of FFT representations reduces the computational time involved in producing the property closures due to the use of fast FFT algorithms. Moreover, FFT algorithms are readily available as opposed to GSH codes. PMID:28793566

High Speed Intact Protein Characterization Using 4X Frequency Multiplication, Ion Trap Harmonization, and 21 Tesla FTICR-MS.

PubMed

Shaw, Jared B; Gorshkov, Mikhail V; Wu, Qinghao; Paša-Tolić, Ljiljana

2018-05-01

Mass spectrometric characterization of large biomolecules, such as intact proteins, requires the specificity afforded by ultrahigh resolution mass measurements performed at both the intact mass and product ion levels. Although the performance of time-of-flight mass analyzers is steadily increasing, the choice of mass analyzer for large biomolecules (e.g., proteins >50 kDa) is generally limited to the Fourier transform family of mass analyzers such as Orbitrap and ion cyclotron resonance (FTICR-MS), with the latter providing unmatched mass resolving power and measurement accuracy. Yet, protein analyses using FTMS are largely hindered by the low acquisition rates of spectra with ultrahigh resolving power. Frequency multiple detection schemes enable FTICR-MS to overcome this fundamental barrier and achieve resolving powers and acquisition speeds 4× greater than the limits imposed by magnetic field strength. Here we expand upon earlier work on the implementation of this technique for biomolecular characterization. We report the coupling of 21T FTICR-MS, 4X frequency multiplication, ion trapping field harmonization technology, and spectral data processing methods to achieve unprecedented acquisition rates and resolving power in mass spectrometry of large intact proteins. Isotopically resolved spectra of multiply charged ubiquitin ions were acquired using detection periods as short as 12 ms. Large proteins such as apo-transferrin (MW = 78 kDa) and monoclonal antibody (MW = 150 kDa) were isotopically resolved with detection periods of 384 and 768 ms, respectively. These results illustrate the future capability of accurate characterization of large proteins on time scales compatible with online separations.

Fourier Transfrom Ion Cyclotron Resonance Mass Spectrometry at High Magnetic Field

NASA Astrophysics Data System (ADS)

Marshall, Alan G.

1998-03-01

At high magnetic field (9.4 tesla at NHMFL), Fourier transform ion cyclotron resonance mass spectrometry performance improves dramatically: mass resolving power, axialization efficiency, and scan speed (each proportional to B), maximum ion mass, dynamic range, ion trapping period, kinetic energy, and electron self-cooling rate for sympathetic cooling (each proportional to B^2), and ion coalescence tendency (proportional 1/B^2). These advantages may apply singly (e.g., unit mass resolution for proteins of >100,000 Da), or compound (e.g., 10-fold improvement in S/N ratio for 9.4 T vs. 6 T at the same resolving power). Examples range from direct determination of molecular formulas of diesel fuel components by accurate mass measurement (=B10.1 ppm) to protein structure and dynamics probed by H/D exchange. This work was supported by N.S.F. (CHE-93-22824; CHE-94-13008), N.I.H. (GM-31683), Florida State University, and the National High Magnetic Field Laboratory in Tallahassee, FL.

Reduction and coding of synthetic aperture radar data with Fourier transforms

NASA Technical Reports Server (NTRS)

Tilley, David G.

1995-01-01

Recently, aboard the Space Radar Laboratory (SRL), the two roles of Fourier Transforms for ocean image synthesis and surface wave analysis have been implemented with a dedicated radar processor to significantly reduce Synthetic Aperture Radar (SAR) ocean data before transmission to the ground. The object was to archive the SAR image spectrum, rather than the SAR image itself, to reduce data volume and capture the essential descriptors of the surface wave field. SAR signal data are usually sampled and coded in the time domain for transmission to the ground where Fourier Transforms are applied both to individual radar pulses and to long sequences of radar pulses to form two-dimensional images. High resolution images of the ocean often contain no striking features and subtle image modulations by wind generated surface waves are only apparent when large ocean regions are studied, with Fourier transforms, to reveal periodic patterns created by wind stress over the surface wave field. Major ocean currents and atmospheric instability in coastal environments are apparent as large scale modulations of SAR imagery. This paper explores the possibility of computing complex Fourier spectrum codes representing SAR images, transmitting the coded spectra to Earth for data archives and creating scenes of surface wave signatures and air-sea interactions via inverse Fourier transformations with ground station processors.

SAR image formation with azimuth interpolation after azimuth transform

DOEpatents

Doerry,; Armin W. , Martin; Grant D. , Holzrichter; Michael, W [Albuquerque, NM

2008-07-08

Two-dimensional SAR data can be processed into a rectangular grid format by subjecting the SAR data to a Fourier transform operation, and thereafter to a corresponding interpolation operation. Because the interpolation operation follows the Fourier transform operation, the interpolation operation can be simplified, and the effect of interpolation errors can be diminished. This provides for the possibility of both reducing the re-grid processing time, and improving the image quality.

Fourier Transforms of Pulses Containing Exponential Leading and Trailing Profiles

DOE Office of Scientific and Technical Information (OSTI.GOV)

Warshaw, S I

2001-07-15

In this monograph we discuss a class of pulse shapes that have exponential rise and fall profiles, and evaluate their Fourier transforms. Such pulses can be used as models for time-varying processes that produce an initial exponential rise and end with the exponential decay of a specified physical quantity. Unipolar examples of such processes include the voltage record of an increasingly rapid charge followed by a damped discharge of a capacitor bank, and the amplitude of an electromagnetic pulse produced by a nuclear explosion. Bipolar examples include acoustic N waves propagating for long distances in the atmosphere that have resultedmore » from explosions in the air, and sonic booms generated by supersonic aircraft. These bipolar pulses have leading and trailing edges that appear to be exponential in character. To the author's knowledge the Fourier transforms of such pulses are not generally well-known or tabulated in Fourier transform compendia, and it is the purpose of this monograph to derive and present these transforms. These Fourier transforms are related to a definite integral of a ratio of exponential functions, whose evaluation we carry out in considerable detail. From this result we derive the Fourier transforms of other related functions. In all Figures showing plots of calculated curves, the actual numbers used for the function parameter values and dependent variables are arbitrary and non-dimensional, and are not identified with any particular physical phenomenon or model.« less

Adaptive Filtering to Enhance Noise Immunity of Impedance and Admittance Spectroscopy: Comparison with Fourier Transformation

NASA Astrophysics Data System (ADS)

Stupin, Daniil D.; Koniakhin, Sergei V.; Verlov, Nikolay A.; Dubina, Michael V.

2017-05-01

The time-domain technique for impedance spectroscopy consists of computing the excitation voltage and current response Fourier images by fast or discrete Fourier transformation and calculating their relation. Here we propose an alternative method for excitation voltage and current response processing for deriving a system impedance spectrum based on a fast and flexible adaptive filtering method. We show the equivalence between the problem of adaptive filter learning and deriving the system impedance spectrum. To be specific, we express the impedance via the adaptive filter weight coefficients. The noise-canceling property of adaptive filtering is also justified. Using the RLC circuit as a model system, we experimentally show that adaptive filtering yields correct admittance spectra and elements ratings in the high-noise conditions when the Fourier-transform technique fails. Providing the additional sensitivity of impedance spectroscopy, adaptive filtering can be applied to otherwise impossible-to-interpret time-domain impedance data. The advantages of adaptive filtering are justified with practical living-cell impedance measurements.

Real-Time and Memory Correlation via Acousto-Optic Processing,

DTIC Science & Technology

1978-06-01

acousto - optic technology as an answer to these requirements appears very attractive. Three fundamental signal-processing schemes using the acousto ... optic interaction have been investigated: (i) real-time correlation and convolution, (ii) Fourier and discrete Fourier transformation, and (iii

A new fractional wavelet transform

NASA Astrophysics Data System (ADS)

Dai, Hongzhe; Zheng, Zhibao; Wang, Wei

2017-03-01

The fractional Fourier transform (FRFT) is a potent tool to analyze the time-varying signal. However, it fails in locating the fractional Fourier domain (FRFD)-frequency contents which is required in some applications. A novel fractional wavelet transform (FRWT) is proposed to solve this problem. It displays the time and FRFD-frequency information jointly in the time-FRFD-frequency plane. The definition, basic properties, inverse transform and reproducing kernel of the proposed FRWT are considered. It has been shown that an FRWT with proper order corresponds to the classical wavelet transform (WT). The multiresolution analysis (MRA) associated with the developed FRWT, together with the construction of the orthogonal fractional wavelets are also presented. Three applications are discussed: the analysis of signal with time-varying frequency content, the FRFD spectrum estimation of signals that involving noise, and the construction of fractional Harr wavelet. Simulations verify the validity of the proposed FRWT.

Short time Fourier analysis of the electromyogram - Fast movements and constant contraction

NASA Technical Reports Server (NTRS)

Hannaford, Blake; Lehman, Steven

1986-01-01

Short-time Fourier analysis was applied to surface electromyograms (EMG) recorded during rapid movements, and during isometric contractions at constant forces. A portion of the data to be transformed by multiplying the signal by a Hamming window was selected, and then the discrete Fourier transform was computed. Shifting the window along the data record, a new spectrum was computed each 10 ms. The transformed data were displayed in spectograms or 'voiceprints'. This short-time technique made it possible to see time-dependencies in the EMG that are normally averaged in the Fourier analysis of these signals. Spectra of EMGs during isometric contractions at constant force vary in the short (10-20 ms) term. Short-time spectra from EMGs recorded during rapid movements were much less variable. The windowing technique picked out the typical 'three-burst pattern' in EMG's from both wrist and head movements. Spectra during the bursts were more consistent than those during isometric contractions. Furthermore, there was a consistent shift in spectral statistics in the course of the three bursts. Both the center frequency and the variance of the spectral energy distribution grew from the first burst to the second burst in the same muscle. The analogy between EMGs and speech signals is extended to argue for future applicability of short-time spectral analysis of EMG.

A Short Biography of Joseph Fourier and Historical Development of Fourier Series and Fourier Transforms

ERIC Educational Resources Information Center

Debnath, Lokenath

2012-01-01

This article deals with a brief biographical sketch of Joseph Fourier, his first celebrated work on analytical theory of heat, his first great discovery of Fourier series and Fourier transforms. Included is a historical development of Fourier series and Fourier transforms with their properties, importance and applications. Special emphasis is made…

Calculation of power spectrums from digital time series with missing data points

NASA Technical Reports Server (NTRS)

Murray, C. W., Jr.

1980-01-01

Two algorithms are developed for calculating power spectrums from the autocorrelation function when there are missing data points in the time series. Both methods use an average sampling interval to compute lagged products. One method, the correlation function power spectrum, takes the discrete Fourier transform of the lagged products directly to obtain the spectrum, while the other, the modified Blackman-Tukey power spectrum, takes the Fourier transform of the mean lagged products. Both techniques require fewer calculations than other procedures since only 50% to 80% of the maximum lags need be calculated. The algorithms are compared with the Fourier transform power spectrum and two least squares procedures (all for an arbitrary data spacing). Examples are given showing recovery of frequency components from simulated periodic data where portions of the time series are missing and random noise has been added to both the time points and to values of the function. In addition the methods are compared using real data. All procedures performed equally well in detecting periodicities in the data.

Autofocus algorithm using one-dimensional Fourier transform and Pearson correlation

NASA Astrophysics Data System (ADS)

Bueno Mario, A.; Alvarez-Borrego, Josue; Acho, L.

2004-10-01

A new autofocus algorithm based on one-dimensional Fourier transform and Pearson correlation for Z automatized microscope is proposed. Our goal is to determine in fast response time and accuracy, the best focused plane through an algorithm. We capture in bright and dark field several images set at different Z distances from biological organism sample. The algorithm uses the one-dimensional Fourier transform to obtain the image frequency content of a vectors pattern previously defined comparing the Pearson correlation of these frequency vectors versus the reference image frequency vector, the most out of focus image, we find the best focusing. Experimental results showed the algorithm has fast response time and accuracy in getting the best focus plane from captured images. In conclusions, the algorithm can be implemented in real time systems due fast response time, accuracy and robustness. The algorithm can be used to get focused images in bright and dark field and it can be extended to include fusion techniques to construct multifocus final images beyond of this paper.

The time-resolved photoelectron spectrum of toluene using a perturbation theory approach

DOE Office of Scientific and Technical Information (OSTI.GOV)

Richings, Gareth W.; Worth, Graham A., E-mail: g.a.worth@bham.ac.uk

A theoretical study of the intra-molecular vibrational-energy redistribution of toluene using time-resolved photo-electron spectra calculated using nuclear quantum dynamics and a simple, two-mode model is presented. Calculations have been carried out using the multi-configuration time-dependent Hartree method, using three levels of approximation for the calculation of the spectra. The first is a full quantum dynamics simulation with a discretisation of the continuum wavefunction of the ejected electron, whilst the second uses first-order perturbation theory to calculate the wavefunction of the ion. Both methods rely on the explicit inclusion of both the pump and probe laser pulses. The third method includesmore » only the pump pulse and generates the photo-electron spectrum by projection of the pumped wavepacket onto the ion potential energy surface, followed by evaluation of the Fourier transform of the autocorrelation function of the subsequently propagated wavepacket. The calculations performed have been used to study the periodic population flow between the 6a and 10b16b modes in the S{sub 1} excited state, and compared to recent experimental data. We obtain results in excellent agreement with the experiment and note the efficiency of the perturbation method.« less

Silicon drift detectors as a tool for time-resolved fluorescence XAFS on low-concentrated samples in catalysis.

PubMed

Kappen, Peter; Tröger, Larc; Materlik, Gerhard; Reckleben, Christian; Hansen, Karsten; Grunwaldt, Jan-Dierk; Clausen, Bjerne S

2002-07-01

A silicon drift detector (SDD) was used for ex situ and time-resolved in situ fluorescence X-ray absorption fine structure (XAFS) on low-concentrated catalyst samples. For a single-element and a seven-element SDD the energy resolution and the peak-to-background ratio were verified at high count rates, sufficient for fluorescence XAFS. An experimental set-up including the seven-element SDD without any cooling and an in situ cell with gas supply and on-line gas analysis was developed. With this set-up the reduction and oxidation of a zeolite supported catalyst containing 0.3 wt% platinum was followed by fluorescence near-edge scans with a time resolution of 10 min each. From ex situ experiments on low-concentrated platinum- and gold-based catalysts fluorescence XAFS scans could be obtained with sufficient statistical quality for a quantitative analysis. Structural information on the gold and platinum particles could be extracted by both the Fourier transforms and the near-edge region of the XAFS spectra. Moreover, it was found that with the seven-element SDD concentrations of the element of interest as low as 100 ppm can be examined by fluorescence XAFS.

Nonuniform sampling and non-Fourier signal processing methods in multidimensional NMR

PubMed Central

Mobli, Mehdi; Hoch, Jeffrey C.

2017-01-01

Beginning with the introduction of Fourier Transform NMR by Ernst and Anderson in 1966, time domain measurement of the impulse response (the free induction decay, FID) consisted of sampling the signal at a series of discrete intervals. For compatibility with the discrete Fourier transform (DFT), the intervals are kept uniform, and the Nyquist theorem dictates the largest value of the interval sufficient to avoid aliasing. With the proposal by Jeener of parametric sampling along an indirect time dimension, extension to multidimensional experiments employed the same sampling techniques used in one dimension, similarly subject to the Nyquist condition and suitable for processing via the discrete Fourier transform. The challenges of obtaining high-resolution spectral estimates from short data records using the DFT were already well understood, however. Despite techniques such as linear prediction extrapolation, the achievable resolution in the indirect dimensions is limited by practical constraints on measuring time. The advent of non-Fourier methods of spectrum analysis capable of processing nonuniformly sampled data has led to an explosion in the development of novel sampling strategies that avoid the limits on resolution and measurement time imposed by uniform sampling. The first part of this review discusses the many approaches to data sampling in multidimensional NMR, the second part highlights commonly used methods for signal processing of such data, and the review concludes with a discussion of other approaches to speeding up data acquisition in NMR. PMID:25456315

Sub-5-ps optical pulse generation from a 1.55-µm distributed-feedback laser diode with nanosecond electric pulse excitation and spectral filtering.

PubMed

Chen, Shaoqiang; Sato, Aya; Ito, Takashi; Yoshita, Masahiro; Akiyama, Hidefumi; Yokoyama, Hiroyuki

2012-10-22

This paper reports generation of sub-5-ps Fourier-transform limited optical pulses from a 1.55-µm gain-switched single-mode distributed-feedback laser diode via nanosecond electric excitation and a simple spectral-filtering technique. Typical damped oscillations of the whole lasing spectrum were observed in the time-resolved waveform. Through a spectral-filtering technique, the initial relaxation oscillation pulse and the following components in the output pulse can be well separated, and the initial short pulse can be selectively extracted by filtering out the short-wavelength components in the spectrum. Short pulses generated by this simple method are expected to have wide potential applications comparable to mode-locking lasers.

Simultaneous multi-beam planar array IR (pair) spectroscopy

DOEpatents

Elmore, Douglas L.; Rabolt, John F.; Tsao, Mei-Wei

2005-09-13

An apparatus and method capable of providing spatially multiplexed IR spectral information simultaneously in real-time for multiple samples or multiple spatial areas of one sample using IR absorption phenomena requires no moving parts or Fourier Transform during operation, and self-compensates for background spectra and degradation of component performance over time. IR spectral information and chemical analysis of the samples is determined by using one or more IR sources, sampling accessories for positioning the samples, optically dispersive elements, a focal plane array (FPA) arranged to detect the dispersed light beams, and a processor and display to control the FPA, and display an IR spectrograph. Fiber-optic coupling can be used to allow remote sensing. Portability, reliability, and ruggedness is enhanced due to the no-moving part construction. Applications include determining time-resolved orientation and characteristics of materials, including polymer monolayers. Orthogonal polarizers may be used to determine certain material characteristics.

CIDEP study on the flash photolysis of benzoin included in β-cyclodextrin

NASA Astrophysics Data System (ADS)

Kitahama, Yasutaka; Murai, Hisao

1996-10-01

The photodissociation reaction of benzoin (Norrish type I) included in a β-cyclodextrin (CD) cavity in the aqueous phase was studied by using time-resolved ESR and Fourier transform ESR methods. The CIDEP (chemically induced dynamic electron polarization) spectra of α-hydroxybenzyl radical and benzoyl radical were carefully investigated in β-CD, in ethanol, in an ethanol/water mixture, and in saturated aqueous solutions. According to these data and the calculations due to an extended Bloch equation, the spin-lattice relaxation time observed in the β-CD system was compared to those in homogeneous solutions. It is concluded that dissociation takes place from the excited triplet state of benzoin and the fragment radicals are easily ejected from the cavity of β-CD to the aqueous phase much faster than the time-resolution (˜ 20 ns) of the present FT-ESR measurement.

Mapping agroecological zones and time lag in vegetation growth by means of Fourier analysis of time series of NDVI images

NASA Technical Reports Server (NTRS)

Menenti, M.; Azzali, S.; Verhoef, W.; Van Swol, R.

1993-01-01

Examples are presented of applications of a fast Fourier transform algorithm to analyze time series of images of Normalized Difference Vegetation Index values. The results obtained for a case study on Zambia indicated that differences in vegetation development among map units of an existing agroclimatic map were not significant, while reliable differences were observed among the map units obtained using the Fourier analysis.

GPU-accelerated non-uniform fast Fourier transform-based compressive sensing spectral domain optical coherence tomography.

PubMed

Xu, Daguang; Huang, Yong; Kang, Jin U

2014-06-16

We implemented the graphics processing unit (GPU) accelerated compressive sensing (CS) non-uniform in k-space spectral domain optical coherence tomography (SD OCT). Kaiser-Bessel (KB) function and Gaussian function are used independently as the convolution kernel in the gridding-based non-uniform fast Fourier transform (NUFFT) algorithm with different oversampling ratios and kernel widths. Our implementation is compared with the GPU-accelerated modified non-uniform discrete Fourier transform (MNUDFT) matrix-based CS SD OCT and the GPU-accelerated fast Fourier transform (FFT)-based CS SD OCT. It was found that our implementation has comparable performance to the GPU-accelerated MNUDFT-based CS SD OCT in terms of image quality while providing more than 5 times speed enhancement. When compared to the GPU-accelerated FFT based-CS SD OCT, it shows smaller background noise and less side lobes while eliminating the need for the cumbersome k-space grid filling and the k-linear calibration procedure. Finally, we demonstrated that by using a conventional desktop computer architecture having three GPUs, real-time B-mode imaging can be obtained in excess of 30 fps for the GPU-accelerated NUFFT based CS SD OCT with frame size 2048(axial) × 1,000(lateral).

A Discussion of the Discrete Fourier Transform Execution on a Typical Desktop PC

NASA Technical Reports Server (NTRS)

White, Michael J.

2006-01-01

This paper will discuss and compare the execution times of three examples of the Discrete Fourier Transform (DFT). The first two examples will demonstrate the direct implementation of the algorithm. In the first example, the Fourier coefficients are generated at the execution of the DFT. In the second example, the coefficients are generated prior to execution and the DFT coefficients are indexed at execution. The last example will demonstrate the Cooley- Tukey algorithm, better known as the Fast Fourier Transform. All examples were written in C executed on a PC using a Pentium 4 running at 1.7 Ghz. As a function of N, the total complex data size, the direct implementation DFT executes, as expected at order of N2 and the FFT executes at order of N log2 N. At N=16K, there is an increase in processing time beyond what is expected. This is not caused by implementation but is a consequence of the effect that machine architecture and memory hierarchy has on implementation. This paper will include a brief overview of digital signal processing, along with a discussion of contemporary work with discrete Fourier processing.

Two-dimensional fourier transform spectrometer

DOEpatents

DeFlores, Lauren; Tokmakoff, Andrei

2016-10-25

The present invention relates to a system and methods for acquiring two-dimensional Fourier transform (2D FT) spectra. Overlap of a collinear pulse pair and probe induce a molecular response which is collected by spectral dispersion of the signal modulated probe beam. Simultaneous collection of the molecular response, pulse timing and characteristics permit real time phasing and rapid acquisition of spectra. Full spectra are acquired as a function of pulse pair timings and numerically transformed to achieve the full frequency-frequency spectrum. This method demonstrates the ability to acquire information on molecular dynamics, couplings and structure in a simple apparatus. Multi-dimensional methods can be used for diagnostic and analytical measurements in the biological, biomedical, and chemical fields.

Two-dimensional fourier transform spectrometer

DOEpatents

DeFlores, Lauren; Tokmakoff, Andrei

2013-09-03

The present invention relates to a system and methods for acquiring two-dimensional Fourier transform (2D FT) spectra. Overlap of a collinear pulse pair and probe induce a molecular response which is collected by spectral dispersion of the signal modulated probe beam. Simultaneous collection of the molecular response, pulse timing and characteristics permit real time phasing and rapid acquisition of spectra. Full spectra are acquired as a function of pulse pair timings and numerically transformed to achieve the full frequency-frequency spectrum. This method demonstrates the ability to acquire information on molecular dynamics, couplings and structure in a simple apparatus. Multi-dimensional methods can be used for diagnostic and analytical measurements in the biological, biomedical, and chemical fields.

[Spatial domain display for interference image dataset].

PubMed

Wang, Cai-Ling; Li, Yu-Shan; Liu, Xue-Bin; Hu, Bing-Liang; Jing, Juan-Juan; Wen, Jia

2011-11-01

The requirements of imaging interferometer visualization is imminent for the user of image interpretation and information extraction. However, the conventional researches on visualization only focus on the spectral image dataset in spectral domain. Hence, the quick show of interference spectral image dataset display is one of the nodes in interference image processing. The conventional visualization of interference dataset chooses classical spectral image dataset display method after Fourier transformation. In the present paper, the problem of quick view of interferometer imager in image domain is addressed and the algorithm is proposed which simplifies the matter. The Fourier transformation is an obstacle since its computation time is very large and the complexion would be even deteriorated with the size of dataset increasing. The algorithm proposed, named interference weighted envelopes, makes the dataset divorced from transformation. The authors choose three interference weighted envelopes respectively based on the Fourier transformation, features of interference data and human visual system. After comparing the proposed with the conventional methods, the results show the huge difference in display time.

The use of spectral methods in bidomain studies.

PubMed

Trayanova, N; Pilkington, T

1992-01-01

A Fourier transform method is developed for solving the bidomain coupled differential equations governing the intracellular and extracellular potentials on a finite sheet of cardiac cells undergoing stimulation. The spectral formulation converts the system of differential equations into a "diagonal" system of algebraic equations. Solving the algebraic equations directly and taking the inverse transform of the potentials proved numerically less expensive than solving the coupled differential equations by means of traditional numerical techniques, such as finite differences; the comparison between the computer execution times showed that the Fourier transform method was about 40 times faster than the finite difference method. By application of the Fourier transform method, transmembrane potential distributions in the two-dimensional myocardial slice were calculated. For a tissue characterized by a ratio of the intra- to extracellular conductivities that is different in all principal directions, the transmembrane potential distribution exhibits a rather complicated geometrical pattern. The influence of the different anisotropy ratios, the finite tissue size, and the stimuli configuration on the pattern of membrane polarization is investigated.

Thermal stabilization of static single-mirror Fourier transform spectrometers

NASA Astrophysics Data System (ADS)

Schardt, Michael; Schwaller, Christian; Tremmel, Anton J.; Koch, Alexander W.

2017-05-01

Fourier transform spectroscopy has become a standard method for spectral analysis of infrared light. With this method, an interferogram is created by two beam interference which is subsequently Fourier-transformed. Most Fourier transform spectrometers used today provide the interferogram in the temporal domain. In contrast, static Fourier transform spectrometers generate interferograms in the spatial domain. One example of this type of spectrometer is the static single-mirror Fourier transform spectrometer which offers a high etendue in combination with a simple, miniaturized optics design. As no moving parts are required, it also features a high vibration resistance and high measurement rates. However, it is susceptible to temperature variations. In this paper, we therefore discuss the main sources for temperature-induced errors in static single-mirror Fourier transform spectrometers: changes in the refractive index of the optical components used, variations of the detector sensitivity, and thermal expansion of the housing. As these errors manifest themselves in temperature-dependent wavenumber shifts and intensity shifts, they prevent static single-mirror Fourier transform spectrometers from delivering long-term stable spectra. To eliminate these shifts, we additionally present a work concept for the thermal stabilization of the spectrometer. With this stabilization, static single-mirror Fourier transform spectrometers are made suitable for infrared process spectroscopy under harsh thermal environmental conditions. As the static single-mirror Fourier transform spectrometer uses the so-called source-doubling principle, many of the mentioned findings are transferable to other designs of static Fourier transform spectrometers based on the same principle.

Transfer Function Identification Using Orthogonal Fourier Transform Modeling Functions

NASA Technical Reports Server (NTRS)

Morelli, Eugene A.

2013-01-01

A method for transfer function identification, including both model structure determination and parameter estimation, was developed and demonstrated. The approach uses orthogonal modeling functions generated from frequency domain data obtained by Fourier transformation of time series data. The method was applied to simulation data to identify continuous-time transfer function models and unsteady aerodynamic models. Model fit error, estimated model parameters, and the associated uncertainties were used to show the effectiveness of the method for identifying accurate transfer function models from noisy data.

Conformational study of 2-phenylethylamine by molecular-beam Fourier transform microwave spectroscopy.

PubMed

López, Juan C; Cortijo, Vanessa; Blanco, Susana; Alonso, Jose L

2007-08-28

The conformational preferences of the simplest amine neurotransmitter 2-phenylethylamine have been investigated using molecular beam Fourier transform microwave (MB-FTMW) spectroscopy. Two new conformers have been observed together with the two previously reported by Godfrey et al. [J. Am. Chem. Soc., 1995, 117, 8204]. The (14)N nuclear quadrupole hyperfine structure has been resolved for all four conformers. Comparison of the experimental rotational and quadrupole coupling constants with those calculated theoretically provides a conclusive test for the identification of all conformers. The two most stable conformers present a gauche (folded) disposition of the alkyl-amine chain and are stabilised by a weak NH...pi interaction between the amino group and the aromatic ring. The other two conformers show an anti (extended) arrangement of the alkyl-amine chain. Tunnelling splittings have been observed in the spectrum of one of the anti conformers. The post expansion relative abundances in the supersonic jet have been also investigated and related to the conformer energies.

Fragmentation studies of fulvic acids using collision induced dissociation fourier transform ion cyclotron resonance mass spectrometry.

PubMed

Witt, Matthias; Fuchser, Jens; Koch, Boris P

2009-04-01

The complex natural organic matter standard Suwannee river fulvic acid (SRFA) was analyzed by negative ion mode electrospray ionization Fourier transform ion cyclotron resonance mass spectrometry (ESI FTICR MS) using on-resonance collision induced dissociation (CID) of single ultrahigh resolved mass peaks in the ICR cell. Molecular formula assignment of precursor masses resulted in exactly one molecular formula for each of the peaks. Analyses of the corresponding fragment spectra and comparison to different standard substances revealed specific neutral losses and fragmentation patterns which result in structures consisting of a high degree of carboxyl- and fewer hydroxyl groups. The comparison of fragmented mass peaks within different pseudohomologous series (CH(2)-series, and CH(4) vs O exchange) suggested structurally based differences between these series. CID FTICR MS allowed isolating single mass peaks in a very complex natural organic matter spectrum. Subsequently, fragmentation gave structural insights into this material. Our results suggest that the structural diversity in complex humic substances is not as high as expected.

Hyperspectral infrared nanoimaging of organic samples based on Fourier transform infrared nanospectroscopy

PubMed Central

Amenabar, Iban; Poly, Simon; Goikoetxea, Monika; Nuansing, Wiwat; Lasch, Peter; Hillenbrand, Rainer

2017-01-01

Infrared nanospectroscopy enables novel possibilities for chemical and structural analysis of nanocomposites, biomaterials or optoelectronic devices. Here we introduce hyperspectral infrared nanoimaging based on Fourier transform infrared nanospectroscopy with a tunable bandwidth-limited laser continuum. We describe the technical implementations and present hyperspectral infrared near-field images of about 5,000 pixel, each one covering the spectral range from 1,000 to 1,900 cm−1. To verify the technique and to demonstrate its application potential, we imaged a three-component polymer blend and a melanin granule in a human hair cross-section, and demonstrate that multivariate data analysis can be applied for extracting spatially resolved chemical information. Particularly, we demonstrate that distribution and chemical interaction between the polymer components can be mapped with a spatial resolution of about 30 nm. We foresee wide application potential of hyperspectral infrared nanoimaging for valuable chemical materials characterization and quality control in various fields ranging from materials sciences to biomedicine. PMID:28198384

Identification of trace additives in polymer materials by attenuated total reflection Fourier transform infrared mapping coupled with multivariate curve resolution

NASA Astrophysics Data System (ADS)

Li, Qian; Tang, Yongjiao; Yan, Zhiwei; Zhang, Pudun

2017-06-01

Although multivariate curve resolution (MCR) has been applied to the analysis of Fourier transform infrared (FTIR) imaging, it is still problematic to determine the number of components. The reported methods at present tend to cause the components of low concentration missed. In this paper a new idea was proposed to resolve this problem. First, MCR calculation was repeated by increasing the number of components sequentially, then each retrieved pure spectrum of as-resulted MCR component was directly compared with a real-world pixel spectrum of the local high concentration in the corresponding MCR map. One component was affirmed only if the characteristic bands of the MCR component had been included in its pixel spectrum. This idea was applied to attenuated total reflection (ATR)/FTIR mapping for identifying the trace additives in blind polymer materials and satisfactory results were acquired. The successful demonstration of this novel approach opens up new possibilities for analyzing additives in polymer materials.

Hyperspectral infrared nanoimaging of organic samples based on Fourier transform infrared nanospectroscopy

NASA Astrophysics Data System (ADS)

Amenabar, Iban; Poly, Simon; Goikoetxea, Monika; Nuansing, Wiwat; Lasch, Peter; Hillenbrand, Rainer

2017-02-01

Infrared nanospectroscopy enables novel possibilities for chemical and structural analysis of nanocomposites, biomaterials or optoelectronic devices. Here we introduce hyperspectral infrared nanoimaging based on Fourier transform infrared nanospectroscopy with a tunable bandwidth-limited laser continuum. We describe the technical implementations and present hyperspectral infrared near-field images of about 5,000 pixel, each one covering the spectral range from 1,000 to 1,900 cm-1. To verify the technique and to demonstrate its application potential, we imaged a three-component polymer blend and a melanin granule in a human hair cross-section, and demonstrate that multivariate data analysis can be applied for extracting spatially resolved chemical information. Particularly, we demonstrate that distribution and chemical interaction between the polymer components can be mapped with a spatial resolution of about 30 nm. We foresee wide application potential of hyperspectral infrared nanoimaging for valuable chemical materials characterization and quality control in various fields ranging from materials sciences to biomedicine.

Continued Development of a Planetary Imaging Fourier Transform Spectrometer (PIFTS)

NASA Technical Reports Server (NTRS)

Sromovsky, L. A.

2002-01-01

This report describes continued efforts to evaluate a breadboard of a Planetary Imaging Fourier Transform Spectrometer (PIFTS). The PIFTS breadboard was developed under prior PIDDP funding. That effort is described in the final report for NASA Grant NAG5-6248 and in two conference papers (Sromovsky et al. 2000; Revercomb et al. 2000). The PIFTS breadboard was designed for near-IR (1-5.2 micrometer imaging of planetary targets with spectral resolving powers of several hundred to several thousand, using an InSb detector array providing at least 64x64 pixels imaging detail. The major focus of the development effort was to combine existing technologies to produce a small and low power design compatible with a very low mass flyable instrument. The objective of this grant (NAG5-10729) was further characterization of the breadboard performance, including intercomparisons with the highly accurate non-imaging Advanced Emitted Radiance Interferometer (AERI) (Revercomb et al. 1994; Best et al. 1997).

Hosting a Fourier Transform Spectrometer (FTS) on CubeSat Spacecraft Platforms for Global Measurements of Three-Dimensional Winds

NASA Astrophysics Data System (ADS)

Scott, D. K.; Neilsen, T. L.; Weston, C.; Frazier, C.; Smith, T.; Shumway, A.

2015-12-01

Global measurements of vertically-resolved atmospheric wind profiles offer the potential for improved weather forecasts and superior predictions of atmospheric wind patterns. A small-satellite constellation that uses a Fourier Transform Spectrometer (FTS) instrument onboard 12U CubeSats can provide measurements of global tropospheric wind profiles from space at a very low cost. These small satellites are called FTS CubeSats. This presentation will describe a spacecraft concept that provides a stable, robust platform to host the FTS payload. Of importance to the payload are power, data, station keeping, thermal, and accommodations that enable high spectral measurements to be made from a LEO orbit. The spacecraft concept draws on Space Dynamics Laboratory (SDL) heritage and the recent success of the Dynamic Ionosphere Cubesat Experiment (DICE) and HyperAngular Rainbow Polarimeter (HARP) missions. Working with team members, SDL built a prototype observatory (spacecraft and payload) for testing and proof of concept.

Fast neutral beam ion source coupled to a Fourier transform ion cyclotron resonance mass spectrometer

NASA Astrophysics Data System (ADS)

Hill, Nicholas C.; Limbach, Patrick A.; Shomo, Ronald E., II; Marshall, Alan G.; Appelhans, Anthony D.; Delmore, James E.

1991-11-01

The coupling of an autoneutralizing SF-6 fast ion-beam gun to a Fourier transform ion cyclotron resonance (FT/ICR) mass spectrometer is described. The fast neutral beam provides for secondary-ion-type FT/ICR mass analysis [e.g., production of abundant pseudomolecular (M+H)+ ions] of involatile samples without the need for external ion injection, since ions are formed at the entrance to the ICR ion trap. The design, construction, and testing of the hybrid instrument are described. The feasibility of the experiment (for both broadband and high-resolution FT/ICR positive-ion mass spectra) is demonstrated with tetra-butylammonium bromide and a Tylenol■ sample. The ability to analyze high molecular weight polymers with high mass resolution is demonstrated for Teflon■. All of the advantages of the fast neutral beam ion source previously demonstrated with quadrupole mass analysis are preserved, and the additional advantages of FT/ICR mass analysis (e.g., high mass resolving power, ion trapping) are retained.

Program for the analysis of time series. [by means of fast Fourier transform algorithm

NASA Technical Reports Server (NTRS)

Brown, T. J.; Brown, C. G.; Hardin, J. C.

1974-01-01

A digital computer program for the Fourier analysis of discrete time data is described. The program was designed to handle multiple channels of digitized data on general purpose computer systems. It is written, primarily, in a version of FORTRAN 2 currently in use on CDC 6000 series computers. Some small portions are written in CDC COMPASS, an assembler level code. However, functional descriptions of these portions are provided so that the program may be adapted for use on any facility possessing a FORTRAN compiler and random-access capability. Properly formatted digital data are windowed and analyzed by means of a fast Fourier transform algorithm to generate the following functions: (1) auto and/or cross power spectra, (2) autocorrelations and/or cross correlations, (3) Fourier coefficients, (4) coherence functions, (5) transfer functions, and (6) histograms.

The Fourier analysis of biological transients.

PubMed

Harris, C M

1998-08-31

With modern computing technology the digital implementation of the Fourier transform is widely available, mostly in the form of the fast Fourier transform (FFT). Although the FFT has become almost synonymous with the Fourier transform, it is a fast numerical technique for computing the discrete Fourier transform (DFT) of a finite sequence of sampled data. The DFT is not directly equivalent to the continuous Fourier transform of the underlying biological signal, which becomes important when analyzing biological transients. Although this distinction is well known by some, for many it leads to confusion in how to interpret the FFT of biological data, and in how to precondition data so as to yield a more accurate Fourier transform using the FFT. We review here the fundamentals of Fourier analysis with emphasis on the analysis of transient signals. As an example of a transient, we consider the human saccade to illustrate the pitfalls and advantages of various Fourier analyses.

Real-time and high accuracy frequency measurements for intermediate frequency narrowband signals

NASA Astrophysics Data System (ADS)

Tian, Jing; Meng, Xiaofeng; Nie, Jing; Lin, Liwei

2018-01-01

Real-time and accurate measurements of intermediate frequency signals based on microprocessors are difficult due to the computational complexity and limited time constraints. In this paper, a fast and precise methodology based on the sigma-delta modulator is designed and implemented by first generating the twiddle factors using the designed recursive scheme. This scheme requires zero times of multiplications and only half amounts of addition operations by using the discrete Fourier transform (DFT) and the combination of the Rife algorithm and Fourier coefficient interpolation as compared with conventional methods such as DFT and Fast Fourier Transform. Experimentally, when the sampling frequency is 10 MHz, the real-time frequency measurements with intermediate frequency and narrowband signals have a measurement mean squared error of ±2.4 Hz. Furthermore, a single measurement of the whole system only requires approximately 0.3 s to achieve fast iteration, high precision, and less calculation time.

Two-window heterodyne methods to characterize light fields

NASA Astrophysics Data System (ADS)

Reil, Frank

In this dissertation, I develop a novel Two-Window heterodyne technique for measuring the time-resolved Wigner function of light fields, which allows their complete characterization. A Wigner function is a quasi-probability density that describes the transverse position and transverse momentum of a light field and is Fourier-transform related to its mutual coherence function. It obeys rigorous transport equations and therefore provides an ideal way to characterize a light field and its propagation through various media. I first present the experimental setup of our Two-Window technique, which is based on a heterodyne scheme involving two phase-coupled Local Oscillator beams we call the Dual-LO. The Dual-LO consists of a focused beam ('SLO') which sets the spatial resolution, and a collimated beam ('BLO') which sets the momental resolution. The resolution in transverse position and transverse momentum can be adjusted individually by the size of the SLO and BLO, which enables a measurement resolution surpassing the uncertainty principle associated with Fourier-transform pairs which limits the resolution when just a single LO is used. We first use our technique to determine the beam size, transverse coherence length and radius of curvature of a Gaussian-Schell beam, as well as its longitudinal characteristics, which are related to its optical spectrum. We then examine Enhanced Backscattering at various path-lengths in the turbid medium. For the first time ever, we demonstrate the phase-conjugating properties of a turbid medium by observing the change in sign of the radius of curvature for a non-collimated field incident on the medium. We also perform time-resolved measurements in the transmission regime. In tenuous media we observe two peaks in phase-space confined by a hyperbola which are due to low-order scattering. Their distance depends on the chosen path-delay. Some coherence and even spatial properties of the incident field are preserved in those peaks as measurements with our Two-Window technique show. Various other applications are presented in less detail, such as the Wigner function of the field inside a speckle produced by a piece of glass containing air bubbles.

Fourier transform magnitudes are unique pattern recognition templates.

PubMed

Gardenier, P H; McCallum, B C; Bates, R H

1986-01-01

Fourier transform magnitudes are commonly used in the generation of templates in pattern recognition applications. We report on recent advances in Fourier phase retrieval which are relevant to pattern recognition. We emphasise in particular that the intrinsic form of a finite, positive image is, in general, uniquely related to the magnitude of its Fourier transform. We state conditions under which the Fourier phase can be reconstructed from samples of the Fourier magnitude, and describe a method of achieving this. Computational examples of restoration of Fourier phase (and hence, by Fourier transformation, the intrinsic form of the image) from samples of the Fourier magnitude are also presented.

Reducing aberration effect of Fourier transform lens by modifying Fourier spectrum of diffractive optical element in beam shaping optical system.

PubMed

Zhang, Fang; Zhu, Jing; Song, Qiang; Yue, Weirui; Liu, Jingdan; Wang, Jian; Situ, Guohai; Huang, Huijie

2015-10-20

In general, Fourier transform lenses are considered as ideal in the design algorithms of diffractive optical elements (DOEs). However, the inherent aberrations of a real Fourier transform lens disturb the far field pattern. The difference between the generated pattern and the expected design will impact the system performance. Therefore, a method for modifying the Fourier spectrum of DOEs without introducing other optical elements to reduce the aberration effect of the Fourier transform lens is proposed. By applying this method, beam shaping performance is improved markedly for the optical system with a real Fourier transform lens. The experiments carried out with a commercial Fourier transform lens give evidence for this method. The method is capable of reducing the system complexity as well as improving its performance.

Determination of Carbon Dioxide, Carbon Monoxide, and Methane Concentrations in Cigarette Smoke by Fourier Transform Infrared Spectroscopy

ERIC Educational Resources Information Center

Tan, T. L.; Lebron, G. B.

2012-01-01

The integrated absorbance areas of vibrational bands of CO[subscript 2], CO, and CH[subscript 4] gases in cigarette smoke were measured from Fourier transform infrared (FTIR) spectra to derive the partial pressures of these gases at different smoke times. The quantity of the three gas-phase components of cigarette smoke at different smoke times…

Distributed Two-Dimensional Fourier Transforms on DSPs with an Application for Phase Retrieval

NASA Technical Reports Server (NTRS)

Smith, Jeffrey Scott

2006-01-01

Many applications of two-dimensional Fourier Transforms require fixed timing as defined by system specifications. One example is image-based wavefront sensing. The image-based approach has many benefits, yet it is a computational intensive solution for adaptive optic correction, where optical adjustments are made in real-time to correct for external (atmospheric turbulence) and internal (stability) aberrations, which cause image degradation. For phase retrieval, a type of image-based wavefront sensing, numerous two-dimensional Fast Fourier Transforms (FFTs) are used. To meet the required real-time specifications, a distributed system is needed, and thus, the 2-D FFT necessitates an all-to-all communication among the computational nodes. The 1-D floating point FFT is very efficient on a digital signal processor (DSP). For this study, several architectures and analysis of such are presented which address the all-to-all communication with DSPs. Emphasis of this research is on a 64-node cluster of Analog Devices TigerSharc TS-101 DSPs.

Real-time frequency-to-time mapping based on spectrally-discrete chromatic dispersion.

PubMed

Dai, Yitang; Li, Jilong; Zhang, Ziping; Yin, Feifei; Li, Wangzhe; Xu, Kun

2017-07-10

Traditional photonics-assisted real-time Fourier transform (RTFT) usually suffers from limited chromatic dispersion, huge volume, or large time delay and attendant loss. In this paper we propose frequency-to-time mapping (FTM) by spectrally-discrete dispersion to increase frequency sensitivity greatly. The novel media has periodic ON/OFF intensity frequency response while quadratic phase distribution along disconnected channels, which de-chirps matched optical input to repeated Fourier-transform-limited output. Real-time FTM is then obtained within each period. Since only discrete phase retardation rather than continuously-changed true time delay is required, huge equivalent dispersion is then available by compact device. Such FTM is theoretically analyzed, and implementation by cascaded optical ring resonators is proposed. After a numerical example, our theory is demonstrated by a proof-of-concept experiment, where a single loop containing 0.5-meters-long fiber is used. FTM under 400-MHz unambiguous bandwidth and 25-MHz resolution is reported. Highly-sensitive and linear mapping is achieved with 6.25 ps/MHz, equivalent to ~4.6 × 10 4 -km standard single mode fiber. Extended instantaneous bandwidth is expected by ring cascading. Our proposal may provide a promising method for real-time, low-latency Fourier transform.

Fast data reconstructed method of Fourier transform imaging spectrometer based on multi-core CPU

NASA Astrophysics Data System (ADS)

Yu, Chunchao; Du, Debiao; Xia, Zongze; Song, Li; Zheng, Weijian; Yan, Min; Lei, Zhenggang

2017-10-01

Imaging spectrometer can gain two-dimensional space image and one-dimensional spectrum at the same time, which shows high utility in color and spectral measurements, the true color image synthesis, military reconnaissance and so on. In order to realize the fast reconstructed processing of the Fourier transform imaging spectrometer data, the paper designed the optimization reconstructed algorithm with OpenMP parallel calculating technology, which was further used for the optimization process for the HyperSpectral Imager of `HJ-1' Chinese satellite. The results show that the method based on multi-core parallel computing technology can control the multi-core CPU hardware resources competently and significantly enhance the calculation of the spectrum reconstruction processing efficiency. If the technology is applied to more cores workstation in parallel computing, it will be possible to complete Fourier transform imaging spectrometer real-time data processing with a single computer.

Fractional finite Fourier transform.

PubMed

Khare, Kedar; George, Nicholas

2004-07-01

We show that a fractional version of the finite Fourier transform may be defined by using prolate spheroidal wave functions of order zero. The transform is linear and additive in its index and asymptotically goes over to Namias's definition of the fractional Fourier transform. As a special case of this definition, it is shown that the finite Fourier transform may be inverted by using information over a finite range of frequencies in Fourier space, the inversion being sensitive to noise. Numerical illustrations for both forward (fractional) and inverse finite transforms are provided.

Real-time Fourier transformation of lightwave spectra and application in optical reflectometry.

PubMed

Malacarne, Antonio; Park, Yongwoo; Li, Ming; LaRochelle, Sophie; Azaña, José

2015-12-14

We propose and experimentally demonstrate a fiber-optics scheme for real-time analog Fourier transform (FT) of a lightwave energy spectrum, such that the output signal maps the FT of the spectrum of interest along the time axis. This scheme avoids the need for analog-to-digital conversion and subsequent digital signal post-processing of the photo-detected spectrum, thus being capable of providing the desired FT processing directly in the optical domain at megahertz update rates. The proposed concept is particularly attractive for applications requiring FT analysis of optical spectra, such as in many optical Fourier-domain reflectrometry (OFDR), interferometry, spectroscopy and sensing systems. Examples are reported to illustrate the use of the method for real-time OFDR, where the target axial-line profile is directly observed in a single-shot oscilloscope trace, similarly to a time-of-flight measurement, but with a resolution and depth of range dictated by the underlying interferometry scheme.

Topics In Chemical Instrumentation: Fourier Transformations for Chemists Part I. Introduction to the Fourier Transform.

ERIC Educational Resources Information Center

Glasser, L.

1987-01-01

This paper explores how Fourier Transform (FT) mimics spectral transformation, how this property can be exploited to advantage in spectroscopy, and how the FT can be used in data treatment. A table displays a number of important FT serial/spectral pairs related by Fourier Transformations. A bibliography and listing of computer software related to…

Estimation of spectral kurtosis

NASA Astrophysics Data System (ADS)

Sutawanir

2017-03-01

Rolling bearings are the most important elements in rotating machinery. Bearing frequently fall out of service for various reasons: heavy loads, unsuitable lubrications, ineffective sealing. Bearing faults may cause a decrease in performance. Analysis of bearing vibration signals has attracted attention in the field of monitoring and fault diagnosis. Bearing vibration signals give rich information for early detection of bearing failures. Spectral kurtosis, SK, is a parameter in frequency domain indicating how the impulsiveness of a signal varies with frequency. Faults in rolling bearings give rise to a series of short impulse responses as the rolling elements strike faults, SK potentially useful for determining frequency bands dominated by bearing fault signals. SK can provide a measure of the distance of the analyzed bearings from a healthy one. SK provides additional information given by the power spectral density (psd). This paper aims to explore the estimation of spectral kurtosis using short time Fourier transform known as spectrogram. The estimation of SK is similar to the estimation of psd. The estimation falls in model-free estimation and plug-in estimator. Some numerical studies using simulations are discussed to support the methodology. Spectral kurtosis of some stationary signals are analytically obtained and used in simulation study. Kurtosis of time domain has been a popular tool for detecting non-normality. Spectral kurtosis is an extension of kurtosis in frequency domain. The relationship between time domain and frequency domain analysis is establish through power spectrum-autocovariance Fourier transform. Fourier transform is the main tool for estimation in frequency domain. The power spectral density is estimated through periodogram. In this paper, the short time Fourier transform of the spectral kurtosis is reviewed, a bearing fault (inner ring and outer ring) is simulated. The bearing response, power spectrum, and spectral kurtosis are plotted to visualize the pattern of each fault. Keywords: frequency domain Fourier transform, spectral kurtosis, bearing fault

Nonuniform sampling and non-Fourier signal processing methods in multidimensional NMR.

PubMed

Mobli, Mehdi; Hoch, Jeffrey C

2014-11-01

Beginning with the introduction of Fourier Transform NMR by Ernst and Anderson in 1966, time domain measurement of the impulse response (the free induction decay, FID) consisted of sampling the signal at a series of discrete intervals. For compatibility with the discrete Fourier transform (DFT), the intervals are kept uniform, and the Nyquist theorem dictates the largest value of the interval sufficient to avoid aliasing. With the proposal by Jeener of parametric sampling along an indirect time dimension, extension to multidimensional experiments employed the same sampling techniques used in one dimension, similarly subject to the Nyquist condition and suitable for processing via the discrete Fourier transform. The challenges of obtaining high-resolution spectral estimates from short data records using the DFT were already well understood, however. Despite techniques such as linear prediction extrapolation, the achievable resolution in the indirect dimensions is limited by practical constraints on measuring time. The advent of non-Fourier methods of spectrum analysis capable of processing nonuniformly sampled data has led to an explosion in the development of novel sampling strategies that avoid the limits on resolution and measurement time imposed by uniform sampling. The first part of this review discusses the many approaches to data sampling in multidimensional NMR, the second part highlights commonly used methods for signal processing of such data, and the review concludes with a discussion of other approaches to speeding up data acquisition in NMR. Copyright © 2014 Elsevier B.V. All rights reserved.

Computationally efficient method for Fourier transform of highly chirped pulses for laser and parametric amplifier modeling.

PubMed

Andrianov, Alexey; Szabo, Aron; Sergeev, Alexander; Kim, Arkady; Chvykov, Vladimir; Kalashnikov, Mikhail

2016-11-14

We developed an improved approach to calculate the Fourier transform of signals with arbitrary large quadratic phase which can be efficiently implemented in numerical simulations utilizing Fast Fourier transform. The proposed algorithm significantly reduces the computational cost of Fourier transform of a highly chirped and stretched pulse by splitting it into two separate transforms of almost transform limited pulses, thereby reducing the required grid size roughly by a factor of the pulse stretching. The application of our improved Fourier transform algorithm in the split-step method for numerical modeling of CPA and OPCPA shows excellent agreement with standard algorithms.

A simple filter circuit for denoising biomechanical impact signals.

PubMed

Subramaniam, Suba R; Georgakis, Apostolos

2009-01-01

We present a simple scheme for denoising non-stationary biomechanical signals with the aim of accurately estimating their second derivative (acceleration). The method is based on filtering in fractional Fourier domains using well-known low-pass filters in a way that amounts to a time-varying cut-off threshold. The resulting algorithm is linear and its design is facilitated by the relationship between the fractional Fourier transform and joint time-frequency representations. The implemented filter circuit employs only three low-order filters while its efficiency is further supported by the low computational complexity of the fractional Fourier transform. The results demonstrate that the proposed method can denoise the signals effectively and is more robust against noise as compared to conventional low-pass filters.

Simulation of path delay multiplexing-based Fourier transform spectrometer for fiber Bragg grating interrogation.

PubMed

Chelliah, Pandian; Sahoo, Trilochan; Singh, Sheela; Sujatha, Annie

2015-10-20

A Fourier transform spectrometer (FTS) used for interrogating a fiber Bragg grating (FBG) consists of a scanning-type interferometer. The FTS has a broad wavelength range of operation and good multiplexing capability. However, it has poor wavelength resolution and interrogation speed. We propose a modification to the FTS using path delay multiplexing to improve the same. Using this method, spatial resolution and interrogation time can be improved by n times by using n path delays. In this paper, simulation results for n=2, 5 are shown.

Fourier-transform infrared derivative spectroscopy with an improved signal-to-noise ratio.

PubMed

Fetterman, M R

2005-09-01

Infrared derivative spectroscopy is a useful technique for finding peaks hidden in broad spectral features. A data acquisition technique is shown that will improve the signal-to-noise ratio (SNR) of Fourier-transform infrared (FTIR) derivative spectroscopy. Typically, in a FTIR measurement one samples each point for the same time interval. The effect of using a graded time interval is studied. The simulations presented show that the SNR of first-derivative FTIR spectroscopy will improve by 15% and that the SNR of second-derivative FTIR will improve by 34%.

The fractional Fourier transform and applications

NASA Technical Reports Server (NTRS)

Bailey, David H.; Swarztrauber, Paul N.

1991-01-01

This paper describes the 'fractional Fourier transform', which admits computation by an algorithm that has complexity proportional to the fast Fourier transform algorithm. Whereas the discrete Fourier transform (DFT) is based on integral roots of unity e exp -2(pi)i/n, the fractional Fourier transform is based on fractional roots of unity e exp -2(pi)i(alpha), where alpha is arbitrary. The fractional Fourier transform and the corresponding fast algorithm are useful for such applications as computing DFTs of sequences with prime lengths, computing DFTs of sparse sequences, analyzing sequences with noninteger periodicities, performing high-resolution trigonometric interpolation, detecting lines in noisy images, and detecting signals with linearly drifting frequencies. In many cases, the resulting algorithms are faster by arbitrarily large factors than conventional techniques.

The τq-Fourier transform: Covariance and uniqueness

NASA Astrophysics Data System (ADS)

Kalogeropoulos, Nikolaos

2018-05-01

We propose an alternative definition for a Tsallis entropy composition-inspired Fourier transform, which we call “τq-Fourier transform”. We comment about the underlying “covariance” on the set of algebraic fields that motivates its introduction. We see that the definition of the τq-Fourier transform is automatically invertible in the proper context. Based on recent results in Fourier analysis, it turns that the τq-Fourier transform is essentially unique under the assumption of the exchange of the point-wise product of functions with their convolution.

A spectroscopic study of the hydrogen bonding and pi-pi stacking interactions of harmane with quinoline.

PubMed

Balón, M; Guardado, P; Muñoz, M A; Carmona, C

1998-01-01

A spectroscopic (UV-vis, Fourier transform IR, steady state, and time-resolved fluorescence) study of the interactions of the ground and excited singlet states of harmane (1-methyl-9H-pyrido/3,4-b/indole) with quinoline has been carried out in cyclohexane, toluene, and buffered pH=8.7 aqueous solutions. To analyze how the number of rings in the substrate influences these interactions, pyridine and phenanthridine have also been included in this study. In cyclohexane and toluene 1:1 stoichiometric hydrogen-bonded complexes are formed in both the ground and the excited singlet states. As the number of rings of the benzopyridines and the solvent polarity increase hydrogen-bonding interactions weaken and pi-pi van der Waals interactions become apparent.

Beyond Fourier

NASA Astrophysics Data System (ADS)

Hoch, Jeffrey C.

2017-10-01

Non-Fourier methods of spectrum analysis are gaining traction in NMR spectroscopy, driven by their utility for processing nonuniformly sampled data. These methods afford new opportunities for optimizing experiment time, resolution, and sensitivity of multidimensional NMR experiments, but they also pose significant challenges not encountered with the discrete Fourier transform. A brief history of non-Fourier methods in NMR serves to place different approaches in context. Non-Fourier methods reflect broader trends in the growing importance of computation in NMR, and offer insights for future software development.

Hypercomplex Fourier transforms of color images.

PubMed

Ell, Todd A; Sangwine, Stephen J

2007-01-01

Fourier transforms are a fundamental tool in signal and image processing, yet, until recently, there was no definition of a Fourier transform applicable to color images in a holistic manner. In this paper, hypercomplex numbers, specifically quaternions, are used to define a Fourier transform applicable to color images. The properties of the transform are developed, and it is shown that the transform may be computed using two standard complex fast Fourier transforms. The resulting spectrum is explained in terms of familiar phase and modulus concepts, and a new concept of hypercomplex axis. A method for visualizing the spectrum using color graphics is also presented. Finally, a convolution operational formula in the spectral domain is discussed.

Pressure jump relaxation setup with IR detection and millisecond time resolution

NASA Astrophysics Data System (ADS)

Schiewek, Martin; Krumova, Marina; Hempel, Günter; Blume, Alfred

2007-04-01

An instrument is described that allows the use of Fourier transform infrared (FTIR) spectroscopy as a detection system for kinetic processes after a pressure jump of up to 100bars. The pressure is generated using a high performance liquid chromatography (HPLC) pump and water as a pressure transducing medium. A flexible membrane separates the liquid sample in the IR cell from the pressure transducing medium. Two electromagnetic switching valves in the setup enable pressure jumps with a decay time of 4ms. The FTIR spectrometer is configured to measure time resolved spectra in the millisecond time regime using the rapid scan mode. All components are computer controlled. For a demonstration of the capability of the method first results on the kinetics of a phase transition between two lamellar phases of an aqueous phospholipid dispersion are presented. This combination of FTIR spectroscopy with the pressure jump relaxation technique can also be used for other systems which display cooperative transitions with concomitant volume changes.

Quantitative multi-color FRET measurements by Fourier lifetime excitation-emission matrix spectroscopy.

PubMed

Zhao, Ming; Huang, Run; Peng, Leilei

2012-11-19

Förster resonant energy transfer (FRET) is extensively used to probe macromolecular interactions and conformation changes. The established FRET lifetime analysis method measures the FRET process through its effect on the donor lifetime. In this paper we present a method that directly probes the time-resolved FRET signal with frequency domain Fourier lifetime excitation-emission matrix (FLEEM) measurements. FLEEM separates fluorescent signals by their different phonon energy pathways from excitation to emission. The FRET process generates a unique signal channel that is initiated by donor excitation but ends with acceptor emission. Time-resolved analysis of the FRET EEM channel allows direct measurements on the FRET process, unaffected by free fluorophores that might be present in the sample. Together with time-resolved analysis on non-FRET channels, i.e. donor and acceptor EEM channels, time resolved EEM analysis allows precise quantification of FRET in the presence of free fluorophores. The method is extended to three-color FRET processes, where quantification with traditional methods remains challenging because of the significantly increased complexity in the three-way FRET interactions. We demonstrate the time-resolved EEM analysis method with quantification of three-color FRET in incompletely hybridized triple-labeled DNA oligonucleotides. Quantitative measurements of the three-color FRET process in triple-labeled dsDNA are obtained in the presence of free single-labeled ssDNA and double-labeled dsDNA. The results establish a quantification method for studying multi-color FRET between multiple macromolecules in biochemical equilibrium.

Quantitative multi-color FRET measurements by Fourier lifetime excitation-emission matrix spectroscopy

PubMed Central

Zhao, Ming; Huang, Run; Peng, Leilei

2012-01-01

Förster resonant energy transfer (FRET) is extensively used to probe macromolecular interactions and conformation changes. The established FRET lifetime analysis method measures the FRET process through its effect on the donor lifetime. In this paper we present a method that directly probes the time-resolved FRET signal with frequency domain Fourier lifetime excitation-emission matrix (FLEEM) measurements. FLEEM separates fluorescent signals by their different phonon energy pathways from excitation to emission. The FRET process generates a unique signal channel that is initiated by donor excitation but ends with acceptor emission. Time-resolved analysis of the FRET EEM channel allows direct measurements on the FRET process, unaffected by free fluorophores that might be present in the sample. Together with time-resolved analysis on non-FRET channels, i.e. donor and acceptor EEM channels, time resolved EEM analysis allows precise quantification of FRET in the presence of free fluorophores. The method is extended to three-color FRET processes, where quantification with traditional methods remains challenging because of the significantly increased complexity in the three-way FRET interactions. We demonstrate the time-resolved EEM analysis method with quantification of three-color FRET in incompletely hybridized triple-labeled DNA oligonucleotides. Quantitative measurements of the three-color FRET process in triple-labeled dsDNA are obtained in the presence of free single-labeled ssDNA and double-labeled dsDNA. The results establish a quantification method for studying multi-color FRET between multiple macromolecules in biochemical equilibrium. PMID:23187535

A general statistical test for correlations in a finite-length time series.

PubMed

Hanson, Jeffery A; Yang, Haw

2008-06-07

The statistical properties of the autocorrelation function from a time series composed of independently and identically distributed stochastic variables has been studied. Analytical expressions for the autocorrelation function's variance have been derived. It has been found that two common ways of calculating the autocorrelation, moving-average and Fourier transform, exhibit different uncertainty characteristics. For periodic time series, the Fourier transform method is preferred because it gives smaller uncertainties that are uniform through all time lags. Based on these analytical results, a statistically robust method has been proposed to test the existence of correlations in a time series. The statistical test is verified by computer simulations and an application to single-molecule fluorescence spectroscopy is discussed.

PASSIVELY ESTIMATING INDEX OF REFRACTION FOR SPECULAR REFLECTORS USING POLARIMETRIC HYPERSPECTRAL IMAGING

DTIC Science & Technology

2016-12-22

23 6 Band-averaged radiance image with checkerboard is shown in the upper left. The 2-D Fourier transform of the image is...red is 1) that is multiplied by the Fourier transform of the original image. The inverse Fourier transform is then taken to get the final image with...Polarization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 IFTS Imaging Fourier Transform Spectrometer

Scaled nonuniform Fourier transform for image reconstruction in swept source optical coherence tomography

NASA Astrophysics Data System (ADS)

Mezgebo, Biniyam; Nagib, Karim; Fernando, Namal; Kordi, Behzad; Sherif, Sherif

2018-02-01

Swept Source optical coherence tomography (SS-OCT) is an important imaging modality for both medical and industrial diagnostic applications. A cross-sectional SS-OCT image is obtained by applying an inverse discrete Fourier transform (DFT) to axial interferograms measured in the frequency domain (k-space). This inverse DFT is typically implemented as a fast Fourier transform (FFT) that requires the data samples to be equidistant in k-space. As the frequency of light produced by a typical wavelength-swept laser is nonlinear in time, the recorded interferogram samples will not be uniformly spaced in k-space. Many image reconstruction methods have been proposed to overcome this problem. Most such methods rely on oversampling the measured interferogram then use either hardware, e.g., Mach-Zhender interferometer as a frequency clock module, or software, e.g., interpolation in k-space, to obtain equally spaced samples that are suitable for the FFT. To overcome the problem of nonuniform sampling in k-space without any need for interferogram oversampling, an earlier method demonstrated the use of the nonuniform discrete Fourier transform (NDFT) for image reconstruction in SS-OCT. In this paper, we present a more accurate method for SS-OCT image reconstruction from nonuniform samples in k-space using a scaled nonuniform Fourier transform. The result is demonstrated using SS-OCT images of Axolotl salamander eggs.

Criteria for confirming sequence periodicity identified by Fourier transform analysis: application to GCR2, a candidate plant GPCR?

PubMed

Illingworth, Christopher J R; Parkes, Kevin E; Snell, Christopher R; Mullineaux, Philip M; Reynolds, Christopher A

2008-03-01

Methods to determine periodicity in protein sequences are useful for inferring function. Fourier transformation is one approach but care is required to ensure the periodicity is genuine. Here we have shown that empirically-derived statistical tables can be used as a measure of significance. Genuine protein sequences data rather than randomly generated sequences were used as the statistical backdrop. The method has been applied to G-protein coupled receptor (GPCR) sequences, by Fourier transformation of hydrophobicity values, codon frequencies and the extent of over-representation of codon pairs; the latter being related to translational step times. Genuine periodicity was observed in the hydrophobicity whereas the apparent periodicity (as inferred from previously reported measures) in the translation step times was not validated statistically. GCR2 has recently been proposed as the plant GPCR receptor for the hormone abscisic acid. It has homology to the Lanthionine synthetase C-like family of proteins, an observation confirmed by fold recognition. Application of the Fourier transform algorithm to the GCR2 family revealed strongly predicted seven fold periodicity in hydrophobicity, suggesting why GCR2 has been reported to be a GPCR, despite negative indications in most transmembrane prediction algorithms. The underlying multiple sequence alignment, also required for the Fourier transform analysis of periodicity, indicated that the hydrophobic regions around the 7 GXXG motifs commence near the C-terminal end of each of the 7 inner helices of the alpha-toroid and continue to the N-terminal region of the helix. The results clearly explain why GCR2 has been understandably but erroneously predicted to be a GPCR.

Short-time fractional Fourier methods for the time-frequency representation of chirp signals.

PubMed

Capus, Chris; Brown, Keith

2003-06-01

The fractional Fourier transform (FrFT) provides a valuable tool for the analysis of linear chirp signals. This paper develops two short-time FrFT variants which are suited to the analysis of multicomponent and nonlinear chirp signals. Outputs have similar properties to the short-time Fourier transform (STFT) but show improved time-frequency resolution. The FrFT is a parameterized transform with parameter, a, related to chirp rate. The two short-time implementations differ in how the value of a is chosen. In the first, a global optimization procedure selects one value of a with reference to the entire signal. In the second, a values are selected independently for each windowed section. Comparative variance measures based on the Gaussian function are given and are shown to be consistent with the uncertainty principle in fractional domains. For appropriately chosen FrFT orders, the derived fractional domain uncertainty relationship is minimized for Gaussian windowed linear chirp signals. The two short-time FrFT algorithms have complementary strengths demonstrated by time-frequency representations for a multicomponent bat chirp, a highly nonlinear quadratic chirp, and an output pulse from a finite-difference sonar model with dispersive change. These representations illustrate the improvements obtained in using FrFT based algorithms compared to the STFT.

Time and space integrating acousto-optic folded spectrum processing for SETI

NASA Technical Reports Server (NTRS)

Wagner, K.; Psaltis, D.

1986-01-01

Time and space integrating folded spectrum techniques utilizing acousto-optic devices (AOD) as 1-D input transducers are investigated for a potential application as wideband, high resolution, large processing gain spectrum analyzers in the search for extra-terrestrial intelligence (SETI) program. The space integrating Fourier transform performed by a lens channels the coarse spectral components diffracted from an AOD onto an array of time integrating narrowband fine resolution spectrum analyzers. The pulsing action of a laser diode samples the interferometrically detected output, aliasing the fine resolution components to baseband, as required for the subsequent charge coupled devices (CCD) processing. The raster scan mechanism incorporated into the readout of the CCD detector array is used to unfold the 2-D transform, reproducing the desired high resolution Fourier transform of the input signal.

Automated vessel segmentation using cross-correlation and pooled covariance matrix analysis.

PubMed

Du, Jiang; Karimi, Afshin; Wu, Yijing; Korosec, Frank R; Grist, Thomas M; Mistretta, Charles A

2011-04-01

Time-resolved contrast-enhanced magnetic resonance angiography (CE-MRA) provides contrast dynamics in the vasculature and allows vessel segmentation based on temporal correlation analysis. Here we present an automated vessel segmentation algorithm including automated generation of regions of interest (ROIs), cross-correlation and pooled sample covariance matrix analysis. The dynamic images are divided into multiple equal-sized regions. In each region, ROIs for artery, vein and background are generated using an iterative thresholding algorithm based on the contrast arrival time map and contrast enhancement map. Region-specific multi-feature cross-correlation analysis and pooled covariance matrix analysis are performed to calculate the Mahalanobis distances (MDs), which are used to automatically separate arteries from veins. This segmentation algorithm is applied to a dual-phase dynamic imaging acquisition scheme where low-resolution time-resolved images are acquired during the dynamic phase followed by high-frequency data acquisition at the steady-state phase. The segmented low-resolution arterial and venous images are then combined with the high-frequency data in k-space and inverse Fourier transformed to form the final segmented arterial and venous images. Results from volunteer and patient studies demonstrate the advantages of this automated vessel segmentation and dual phase data acquisition technique. Copyright © 2011 Elsevier Inc. All rights reserved.

Electromagnetic pulse propagation in dispersive planar dielectrics.

PubMed

Moten, K; Durney, C H; Stockham, T G

1989-01-01

The responses of a plane-wave pulse train irradiating a lossy dispersive dielectric half-space are investigated. The incident pulse train is expressed as a Fourier series with summing done by the inverse fast Fourier transform. The Fourier series technique is adopted to avoid the many difficulties often encountered in finding the inverse Fourier transform when transform analyses are used. Calculations are made for propagation in pure water, and typical waveforms inside the dielectric half-space are presented. Higher harmonics are strongly attenuated, resulting in a single continuous sinusoidal waveform at the frequency of the fundamental depth in the material. The time-averaged specific absorption rate (SAR) for pulse-train propagation is shown to be the sum of the time-averaged SARs of the individual harmonic components of the pulse train. For the same average power, calculated SARs reveal that pulse trains generally penetrate deeper than carrier-frequency continuous waves but not deeper than continuous waves at frequencies approaching the fundamental of the pulse train. The effects of rise time on the propagating pulse train in the dielectrics are shown and explained. Since most practical pulsed systems are very limited in bandwidth, no pronounced differences between their response and continuous wave (CW) response would be expected. Typical results for pulse-train propagation in arrays of dispersive planar dielectric slabs are presented. Expressing the pulse train as a Fourier series provides a practical way of interpreting the dispersion characteristics from the spectral point of view.

Stress wave calculations in composite plates using the fast Fourier transform.

NASA Technical Reports Server (NTRS)

Moon, F. C.

1973-01-01

The protection of composite turbine fan blades against impact forces has prompted the study of dynamic stresses in composites due to transient loads. The mathematical model treats the laminated plate as an equivalent anisotropic material. The use of Mindlin's approximate theory of crystal plates results in five two-dimensional stress waves. Three of the waves are flexural and two involve in-plane extensional strains. The initial value problem due to a transient distributed transverse force on the plate is solved using Laplace and Fourier transforms. A fast computer program for inverting the two-dimensional Fourier transform is used. Stress contours for various stresses and times after application of load are obtained for a graphite fiber-epoxy matrix composite plate. Results indicate that the points of maximum stress travel along the fiber directions.

High-speed spectral domain optical coherence tomography using non-uniform fast Fourier transform

PubMed Central

Chan, Kenny K. H.; Tang, Shuo

2010-01-01

The useful imaging range in spectral domain optical coherence tomography (SD-OCT) is often limited by the depth dependent sensitivity fall-off. Processing SD-OCT data with the non-uniform fast Fourier transform (NFFT) can improve the sensitivity fall-off at maximum depth by greater than 5dB concurrently with a 30 fold decrease in processing time compared to the fast Fourier transform with cubic spline interpolation method. NFFT can also improve local signal to noise ratio (SNR) and reduce image artifacts introduced in post-processing. Combined with parallel processing, NFFT is shown to have the ability to process up to 90k A-lines per second. High-speed SD-OCT imaging is demonstrated at camera-limited 100 frames per second on an ex-vivo squid eye. PMID:21258551

[Continuum based fast Fourier transform processing of infrared spectrum].

PubMed

Liu, Qing-Jie; Lin, Qi-Zhong; Wang, Qin-Jun; Li, Hui; Li, Shuai

2009-12-01

To recognize ground objects with infrared spectrum, high frequency noise removing is one of the most important phases in spectrum feature analysis and extraction. A new method for infrared spectrum preprocessing was given combining spectrum continuum processing and Fast Fourier Transform (CFFT). Continuum was firstly removed from the noise polluted infrared spectrum to standardize hyper-spectra. Then the spectrum was transformed into frequency domain (FD) with fast Fourier transform (FFT), separating noise information from target information After noise eliminating from useful information with a low-pass filter, the filtered FD spectrum was transformed into time domain (TD) with fast Fourier inverse transform. Finally the continuum was recovered to the spectrum, and the filtered infrared spectrum was achieved. Experiment was performed for chlorite spectrum in USGS polluted with two kinds of simulated white noise to validate the filtering ability of CFFT by contrast with cubic function of five point (CFFP) in time domain and traditional FFT in frequency domain. A circle of CFFP has limited filtering effect, so it should work much with more circles and consume more time to achieve better filtering result. As for conventional FFT, Gibbs phenomenon has great effect on preprocessing result at edge bands because of special character of rock or mineral spectra, while works well at middle bands. Mean squared error of CFFT is 0. 000 012 336 with cut-off frequency of 150, while that of FFT and CFFP is 0. 000 061 074 with cut-off frequency of 150 and 0.000 022 963 with 150 working circles respectively. Besides the filtering result of CFFT can be improved by adjusting the filter cut-off frequency, and has little effect on working time. The CFFT method overcomes the Gibbs problem of FFT in spectrum filtering, and can be more convenient, dependable, and effective than traditional TD filter methods.

High resolution infrared spectroscopy: Some new approaches and applications to planetary atmospheres

NASA Technical Reports Server (NTRS)

Mumma, M. J.

1978-01-01

The principles of spectral line formation and of techniques for retrieval of atmospheric temperature and constituent profiles are discussed. Applications to the atmospheres of Earth, Mars, Venus, and Jupiter are illustrated by results obtained with Fourier transform and infrared heterodyne spectrometers at resolving powers (lambda/delta hyperon lambda of approximately 10,000 and approximately 10 to the seventh power), respectively, showing the high complementarity of spectroscopy at these two widely different resolving powers. The principles of heterodyne spectroscopy are presented and its applications to atmospheric probing and to laboratory spectroscopy are discussed. Direct absorption spectroscopy with tuneable semiconductor lasers is discussed in terms of precision frequency-and line strength-measurements, showing substantial advances in laboratory infrared spectroscopy.

Fourier Transforms Simplified: Computing an Infrared Spectrum from an Interferogram

ERIC Educational Resources Information Center

Hanley, Quentin S.

2012-01-01

Fourier transforms are used widely in chemistry and allied sciences. Examples include infrared, nuclear magnetic resonance, and mass spectroscopies. A thorough understanding of Fourier methods assists the understanding of microscopy, X-ray diffraction, and diffraction gratings. The theory of Fourier transforms has been presented in this "Journal",…

Time-splitting combined with exponential wave integrator fourier pseudospectral method for Schrödinger-Boussinesq system

NASA Astrophysics Data System (ADS)

Liao, Feng; Zhang, Luming; Wang, Shanshan

2018-02-01

In this article, we formulate an efficient and accurate numerical method for approximations of the coupled Schrödinger-Boussinesq (SBq) system. The main features of our method are based on: (i) the applications of a time-splitting Fourier spectral method for Schrödinger-like equation in SBq system, (ii) the utilizations of exponential wave integrator Fourier pseudospectral for spatial derivatives in the Boussinesq-like equation. The scheme is fully explicit and efficient due to fast Fourier transform. The numerical examples are presented to show the efficiency and accuracy of our method.

A New Approach in Time-Frequency Analysis with Applications to Experimental High Range Resolution Radar Data

DTIC Science & Technology

2003-11-01

Distributions In contrast to the linear time-frequency transforms such as the short-time Fourier transform, the Wigner - Ville distribution ( WVD ) is...23 9 Results of nine TFDs: (a) Wigner - Ville distribution , (b) Born-Jordan distribution , (c) Choi-Williams distribution , (d) bilinear TFD...are applied in the Wigner - Ville class of time-frequency transforms and the reassignment methods, which are applied to any time-frequency distribution

Online frequency estimation with applications to engine and generator sets

NASA Astrophysics Data System (ADS)

Manngård, Mikael; Böling, Jari M.

2017-07-01

Frequency and spectral analysis based on the discrete Fourier transform is a fundamental task in signal processing and machine diagnostics. This paper aims at presenting computationally efficient methods for real-time estimation of stationary and time-varying frequency components in signals. A brief survey of the sliding time window discrete Fourier transform and Goertzel filter is presented, and two filter banks consisting of: (i) sliding time window Goertzel filters (ii) infinite impulse response narrow bandpass filters are proposed for estimating instantaneous frequencies. The proposed methods show excellent results on both simulation studies and on a case study using angular speed data measurements of the crankshaft of a marine diesel engine-generator set.

Missing texture reconstruction method based on error reduction algorithm using Fourier transform magnitude estimation scheme.

PubMed

Ogawa, Takahiro; Haseyama, Miki

2013-03-01

A missing texture reconstruction method based on an error reduction (ER) algorithm, including a novel estimation scheme of Fourier transform magnitudes is presented in this brief. In our method, Fourier transform magnitude is estimated for a target patch including missing areas, and the missing intensities are estimated by retrieving its phase based on the ER algorithm. Specifically, by monitoring errors converged in the ER algorithm, known patches whose Fourier transform magnitudes are similar to that of the target patch are selected from the target image. In the second approach, the Fourier transform magnitude of the target patch is estimated from those of the selected known patches and their corresponding errors. Consequently, by using the ER algorithm, we can estimate both the Fourier transform magnitudes and phases to reconstruct the missing areas.

Signal Coherence Recovery Using Acousto-Optic Fourier Transform Architectures

DTIC Science & Technology

1990-06-14

processing of data in ground- and space-based applications. We have implemented a prototype one-dimensional time-integrating acousto - optic (AO) Fourier...theory of optimum coherence recovery (CR) applicable in computation-limited environments. We have demonstrated direct acousto - optic implementation of CR

Optimal fitting of Gaussian-apodized or under-resolved emission lines in Fourier transform spectra providing new insights on the velocity structure of NGC 6720

NASA Astrophysics Data System (ADS)

Martin, Thomas B.; Prunet, Simon; Drissen, Laurent

2016-12-01

An analysis of the kinematics of NGC 6720 is performed on the commissioning data obtained with SITELLE, the Canada-France-Hawaii Telescope's new imaging Fourier transform spectrometer. In order to measure carefully the small broadening effect of a shell expansion on an unresolved emission line, we have determined a computationally robust implementation of the convolution of a Gaussian with a sinc instrumental line shape which avoids arithmetic overflows. This model can be used to measure line broadening of typically a few km s-1 even at low spectral resolution (R < 5000). We have also designed the corresponding set of Gaussian apodizing functions that are now used by ORBS, the SITELLE's reduction pipeline. We have implemented this model in ORCS, a fitting engine for SITELLE's data, and used it to derive the [S II] density map of the central part of the nebula. The study of the broadening of the [N II] lines shows that the main ring and the central lobe are two different shells with different expansion velocities. We have also derived deep and spatially resolved velocity maps of the halo in [N II] and Hα and found that the brightest bubbles are originating from two bipolar structures with a velocity difference of more than 35 km s-1 lying at the poles of a possibly unique halo shell expanding at a velocity of more than 15 km s-1.

The Fourier transforms for the spatially homogeneous Boltzmann equation and Landau equation

NASA Astrophysics Data System (ADS)

Meng, Fei; Liu, Fang

2018-03-01

In this paper, we study the Fourier transforms for two equations arising in the kinetic theory. The first equation is the spatially homogeneous Boltzmann equation. The Fourier transform of the spatially homogeneous Boltzmann equation has been first addressed by Bobylev (Sov Sci Rev C Math Phys 7:111-233, 1988) in the Maxwellian case. Alexandre et al. (Arch Ration Mech Anal 152(4):327-355, 2000) investigated the Fourier transform of the gain operator for the Boltzmann operator in the cut-off case. Recently, the Fourier transform of the Boltzmann equation is extended to hard or soft potential with cut-off by Kirsch and Rjasanow (J Stat Phys 129:483-492, 2007). We shall first establish the relation between the results in Alexandre et al. (2000) and Kirsch and Rjasanow (2007) for the Fourier transform of the Boltzmann operator in the cut-off case. Then we give the Fourier transform of the spatially homogeneous Boltzmann equation in the non cut-off case. It is shown that our results cover previous works (Bobylev 1988; Kirsch and Rjasanow 2007). The second equation is the spatially homogeneous Landau equation, which can be obtained as a limit of the Boltzmann equation when grazing collisions prevail. Following the method in Kirsch and Rjasanow (2007), we can also derive the Fourier transform for Landau equation.

Bispectral Inversion: The Construction of a Time Series from Its Bispectrum

DTIC Science & Technology

1988-04-13

take the inverse transform . Since the goal is to compute a time series given its bispectrum, it would also be nice to stay entirely in the frequency...domain and be able to go directly from the bispectrum to the Fourier transform of the time series without the need to inverse transform continuous...the picture. The approximations arise from representing the bicovariance, which is the inverse transform of a continuous function, by the inverse disrte

Behavioral Context of Call Production by Eastern North Pacific Blue Whales

DTIC Science & Technology

2007-01-25

pairs occurring in a repeated song sequence; B calls from a different blue whale are also evident; spectrogram parameters: fast Fourier transform (FFT...Acoustic data were viewed in spectrogram form ( fast Fourier transform [FFT] length 1 s, 80% overlap, Hanning window) to de- termine the presence of calls...dura- tion to song A and B units (Table 2), but the intermit - tent timing clearly distinguishes them from song. Whales producing singular calls were

A Synthetic Quadrature Phase Detector/Demodulator for Fourier Transform Transform Spectrometers

NASA Technical Reports Server (NTRS)

Campbell, Joel

2008-01-01

A method is developed to demodulate (velocity correct) Fourier transform spectrometer (FTS) data that is taken with an analog to digital converter that digitizes equally spaced in time. This method makes it possible to use simple low cost, high resolution audio digitizers to record high quality data without the need for an event timer or quadrature laser hardware, and makes it possible to use a metrology laser of any wavelength. The reduced parts count and simplicity implementation makes it an attractive alternative in space based applications when compared to previous methods such as the Brault algorithm.

Applications of asynoptic space - Time Fourier transform methods to scanning satellite measurements

NASA Technical Reports Server (NTRS)

Lait, Leslie R.; Stanford, John L.

1988-01-01

A method proposed by Salby (1982) for computing the zonal space-time Fourier transform of asynoptically acquired satellite data is discussed. The method and its relationship to other techniques are briefly described, and possible problems in applying it to real data are outlined. Examples of results obtained using this technique are given which demonstrate its sensitivity to small-amplitude signals. A number of waves are found which have previously been observed as well as two not heretofore reported. A possible extension of the method which could increase temporal and longitudinal resolution is described.

Radar imaging using electromagnetic wave carrying orbital angular momentum

NASA Astrophysics Data System (ADS)

Yuan, Tiezhu; Cheng, Yongqiang; Wang, Hongqiang; Qin, Yuliang; Fan, Bo

2017-03-01

The concept of radar imaging based on orbital angular momentum (OAM) modulation, which has the ability of azimuthal resolution without relative motion, has recently been proposed. We investigate this imaging technique further in greater detail. We first analyze the principle of the technique, accounting for its resolving ability physically. The phase and intensity distributions of the OAM-carrying fields produced by phased uniform circular array antenna, which have significant effects on the imaging results, are investigated. The imaging model shows that the received signal has the form of inverse discrete Fourier transform with the use of OAM and frequency diversities. The two-dimensional Fourier transform is employed to reconstruct the target images in the case of large and small elevation angles. Due to the peculiar phase and intensity characteristics, the small elevation is more suitable for practical application than the large one. The minimum elevation angle is then obtained given the array parameters. The imaging capability is analyzed by means of the point spread function. All results are verified through numerical simulations. The proposed staring imaging technique can achieve extremely high azimuthal resolution with the use of plentiful OAM modes.

Beyond Fourier.

PubMed

Hoch, Jeffrey C

2017-10-01

Non-Fourier methods of spectrum analysis are gaining traction in NMR spectroscopy, driven by their utility for processing nonuniformly sampled data. These methods afford new opportunities for optimizing experiment time, resolution, and sensitivity of multidimensional NMR experiments, but they also pose significant challenges not encountered with the discrete Fourier transform. A brief history of non-Fourier methods in NMR serves to place different approaches in context. Non-Fourier methods reflect broader trends in the growing importance of computation in NMR, and offer insights for future software development. Copyright © 2017 Elsevier Inc. All rights reserved.

Discrete Fourier transforms of nonuniformly spaced data

NASA Technical Reports Server (NTRS)

Swan, P. R.

1982-01-01

Time series or spatial series of measurements taken with nonuniform spacings have failed to yield fully to analysis using the Discrete Fourier Transform (DFT). This is due to the fact that the formal DFT is the convolution of the transform of the signal with the transform of the nonuniform spacings. Two original methods are presented for deconvolving such transforms for signals containing significant noise. The first method solves a set of linear equations relating the observed data to values defined at uniform grid points, and then obtains the desired transform as the DFT of the uniform interpolates. The second method solves a set of linear equations relating the real and imaginary components of the formal DFT directly to those of the desired transform. The results of numerical experiments with noisy data are presented in order to demonstrate the capabilities and limitations of the methods.

Wavenumber-frequency Spectra of Pressure Fluctuations Measured via Fast Response Pressure Sensitive Paint

NASA Technical Reports Server (NTRS)

Panda, J.; Roozeboom, N. H.; Ross, J. C.

2016-01-01

The recent advancement in fast-response Pressure-Sensitive Paint (PSP) allows time-resolved measurements of unsteady pressure fluctuations from a dense grid of spatial points on a wind tunnel model. This capability allows for direct calculations of the wavenumber-frequency (k-?) spectrum of pressure fluctuations. Such data, useful for the vibro-acoustics analysis of aerospace vehicles, are difficult to obtain otherwise. For the present work, time histories of pressure fluctuations on a flat plate subjected to vortex shedding from a rectangular bluff-body were measured using PSP. The light intensity levels in the photographic images were then converted to instantaneous pressure histories by applying calibration constants, which were calculated from a few dynamic pressure sensors placed at selective points on the plate. Fourier transform of the time-histories from a large number of spatial points provided k-? spectra for pressure fluctuations. The data provides first glimpse into the possibility of creating detailed forcing functions for vibro-acoustics analysis of aerospace vehicles, albeit for a limited frequency range.

Microphase Separation Controlled Beta Sheet Crystallization Kinetics in Silk Fibroin Protein.

NASA Astrophysics Data System (ADS)

Hu, Xiao; Lu, Qiang; Kaplan, David; Cebe, Peggy

2009-03-01

We investigate the mechanism of isothermal crystallization kinetics of beta-sheet crystals in silk multiblock fibrous proteins. The Avrami analysis kinetic theory, for studies of synthetic polymer crystal growth, is for the first time extended to investigate protein self-assembly in beta-sheet rich Bombyx mori silk fibroin samples, using time-resolved Fourier transform infrared spectroscopy, differential scanning calorimetry and synchrotron real-time wide-angle X-ray scattering. Results indicate formation of beta sheet crystals in silk proteins is different from the 3-D spherulitic crystal growth found in synthetic homopolymers. Observations by scanning electron microscopy support the view that the protein structures vary during the different stages of crystal growth, and show a microphase separation pattern after chymotrypsin enzyme biodegradation. We present a model to explain the crystallization of the multiblock silk fibroin protein, by analogy to synthetic block copolymers. This model could be widely applicable in other proteins with multiblock (i.e., crystallizable and non-crystallizable) domains.

Super-Resolution for Color Imagery

DTIC Science & Technology

2017-09-01

separately; however, it requires performing the super-resolution computation 3 times. We transform images in the default red, green, blue (RGB) color space...chrominance components based on ARL’s alias-free image upsampling using Fourier-based windowing methods. A reverse transformation is performed on... Transformation from sRGB to CIELAB............................................... 3 Fig. 2 YCbCr mathematical coordinate transformation

A technique to detect periodic and non-periodic ultra-rapid flux time variations with standard radio-astronomical data

NASA Astrophysics Data System (ADS)

Borra, Ermanno F.; Romney, Jonathan D.; Trottier, Eric

2018-06-01

We demonstrate that extremely rapid and weak periodic and non-periodic signals can easily be detected by using the autocorrelation of intensity as a function of time. We use standard radio-astronomical observations that have artificial periodic and non-periodic signals generated by the electronics of terrestrial origin. The autocorrelation detects weak signals that have small amplitudes because it averages over long integration times. Another advantage is that it allows a direct visualization of the shape of the signals, while it is difficult to see the shape with a Fourier transform. Although Fourier transforms can also detect periodic signals, a novelty of this work is that we demonstrate another major advantage of the autocorrelation, that it can detect non-periodic signals while the Fourier transform cannot. Another major novelty of our work is that we use electric fields taken in a standard format with standard instrumentation at a radio observatory and therefore no specialized instrumentation is needed. Because the electric fields are sampled every 15.625 ns, they therefore allow detection of very rapid time variations. Notwithstanding the long integration times, the autocorrelation detects very rapid intensity variations as a function of time. The autocorrelation could also detect messages from Extraterrestrial Intelligence as non-periodic signals.

Study on time-frequency analysis method of very fast transient overvoltage

NASA Astrophysics Data System (ADS)

Li, Shuai; Liu, Shiming; Huang, Qiyan; Fu, Chuanshun

2018-04-01

The operation of the disconnector in the gas insulated substation (GIS) may produce very fast transient overvoltage (VFTO), which has the characteristics of short rise time, short duration, high amplitude and rich frequency components. VFTO can cause damage to GIS and secondary equipment, and the frequency components contained in the VFTO can cause resonance overvoltage inside the transformer, so it is necessary to study the spectral characteristics of the VFTO. From the perspective of signal processing, VFTO is a kind of non-stationary signal, the traditional Fourier transform is difficult to describe its frequency which changes with time, so it is necessary to use time-frequency analysis to analyze VFTO spectral characteristics. In this paper, we analyze the performance of short time Fourier transform (STFT), Wigner-Ville distribution (WVD), pseudo Wigner-Ville distribution (PWVD) and smooth pseudo Wigner-Ville distribution (SPWVD). The results show that SPWVD transform is the best. The time-frequency aggregation of SPWVD is higher than STFT, and it does not have cross-interference terms, which can meet the requirements of VFTO spectrum analysis.

Microcomputer Simulation of a Fourier Approach to Optical Wave Propagation

DTIC Science & Technology

1992-06-01

and transformed input in transform domain). 44 Figure 21. SHFTOUTPUT1 ( inverse transform of product of Bessel filter and transformed input). . . . 44...Figure 22. SHFT OUTPUT2 ( inverse transform of product of ,derivative filter and transformed input).. 45 Figure 23. •tIFT OUTPUT (sum of SHFTOUTPUT1...52 Figure 33. SHFT OUTPUT1 at time slice 1 ( inverse transform of product of Bessel filter and transformed input) .... ............. ... 53

A study of sound generation in subsonic rotors, volume 2

NASA Technical Reports Server (NTRS)

Chalupnik, J. D.; Clark, L. T.

1975-01-01

Computer programs were developed for use in the analysis of sound generation by subsonic rotors. Program AIRFOIL computes the spectrum of radiated sound from a single airfoil immersed in a laminar flow field. Program ROTOR extends this to a rotating frame, and provides a model for sound generation in subsonic rotors. The program also computes tone sound generation due to steady state forces on the blades. Program TONE uses a moving source analysis to generate a time series for an array of forces moving in a circular path. The resultant time series are than Fourier transformed to render the results in spectral form. Program SDATA is a standard time series analysis package. It reads in two discrete time series and forms auto and cross covariances and normalizes these to form correlations. The program then transforms the covariances to yield auto and cross power spectra by means of a Fourier transformation.

Fault detection of gearbox using time-frequency method

NASA Astrophysics Data System (ADS)

Widodo, A.; Satrijo, Dj.; Prahasto, T.; Haryanto, I.

2017-04-01

This research deals with fault detection and diagnosis of gearbox by using vibration signature. In this work, fault detection and diagnosis are approached by employing time-frequency method, and then the results are compared with cepstrum analysis. Experimental work has been conducted for data acquisition of vibration signal thru self-designed gearbox test rig. This test-rig is able to demonstrate normal and faulty gearbox i.e., wears and tooth breakage. Three accelerometers were used for vibration signal acquisition from gearbox, and optical tachometer was used for shaft rotation speed measurement. The results show that frequency domain analysis using fast-fourier transform was less sensitive to wears and tooth breakage condition. However, the method of short-time fourier transform was able to monitor the faults in gearbox. Wavelet Transform (WT) method also showed good performance in gearbox fault detection using vibration signal after employing time synchronous averaging (TSA).

A time-frequency analysis method to obtain stable estimates of magnetotelluric response function based on Hilbert-Huang transform

NASA Astrophysics Data System (ADS)

Cai, Jianhua

2017-05-01

The time-frequency analysis method represents signal as a function of time and frequency, and it is considered a powerful tool for handling arbitrary non-stationary time series by using instantaneous frequency and instantaneous amplitude. It also provides a possible alternative to the analysis of the non-stationary magnetotelluric (MT) signal. Based on the Hilbert-Huang transform (HHT), a time-frequency analysis method is proposed to obtain stable estimates of the magnetotelluric response function. In contrast to conventional methods, the response function estimation is performed in the time-frequency domain using instantaneous spectra rather than in the frequency domain, which allows for imaging the response parameter content as a function of time and frequency. The theory of the method is presented and the mathematical model and calculation procedure, which are used to estimate response function based on HHT time-frequency spectrum, are discussed. To evaluate the results, response function estimates are compared with estimates from a standard MT data processing method based on the Fourier transform. All results show that apparent resistivities and phases, which are calculated from the HHT time-frequency method, are generally more stable and reliable than those determined from the simple Fourier analysis. The proposed method overcomes the drawbacks of the traditional Fourier methods, and the resulting parameter minimises the estimation bias caused by the non-stationary characteristics of the MT data.

Utility of Higher Harmonics in Electrospray Ionization Fourier Transform Electrostatic Linear Ion Trap Mass Spectrometry.

PubMed

Dziekonski, Eric T; Johnson, Joshua T; McLuckey, Scott A

2017-04-18

Mass resolution (M/ΔM fwhm) is observed to linearly increase with harmonic order in a Fourier transform electrostatic linear ion trap (ELIT) mass spectrometer. This behavior was predicted by Grosshans and Marshall for frequency-multiple detection in a Fourier transform ion cyclotron resonance mass spectrometer only for situations when the prominent mechanism for signal decay is ion ejection from the trap. As the analyzer pressure in our ELIT chamber is relatively high, such that collisional scattering and collision-induced dissociation are expected to underlie much of the ion loss, we sought to explore the relationship between harmonic order and mass resolution. Mass resolutions of 36 900 (fundamental), 75 850 (2nd harmonic), and 108 200 (3rd harmonic) were obtained for GdO + (avg. m/z 173.919) with a transient length of 300 ms. To demonstrate that the mass resolution was truly increasing with harmonic order, the unresolved isotopes at the fundamental distribution of cytochrome c +8 (m/z ∼ 1549) were nearly baseline, resolved at the third harmonic (mass resolution ≈ 23 000) with a transient length of only 200 ms. This experiment demonstrates that, when the ion density is sufficiently low, ions with frequency differences of less than 4 Hz remain uncoalesced. Higher harmonics can be used to increase the effective mass resolution for a fixed transient length and thereby may enable the resolution of closely spaced masses, determination of a protein ion's charge state, and study of the onset of peak coalescence when the resolution at the fundamental frequency is insufficient.

Pulsed-laser excitation of acoustic modes in open high-Q photoacoustic resonators for trace gas monitoring: results for C2H4

NASA Astrophysics Data System (ADS)

Brand, Christian; Winkler, Andreas; Hess, Peter; Miklós, András; Bozóki, Zoltán; Sneider, János

1995-06-01

The pulsed excitation of acoustic resonances was studied with a continuously monitoring photoacoustic detector system. Acoustic waves were generated in C2H4/N 2 gas mixtures by light absorption of the pulses from a transversely excited atmospheric CO2 laser. The photoacoustic part consisted of high-Q cylindrical resonators (Q factor 820 for the first radial mode in N2) and two adjoining variable acoustic filter systems. The time-resolved signal was Fourier transformed to a frequency spectrum of high resolution. For the first radial mode a Lorentzian profile was fitted to the measured data. The outside noise suppression and the signal-to-noise ratio were investigated in a normal laboratory environment in the flow-through mode. The acoustic and electric filter system combined with the

Improvements to surrogate data methods for nonstationary time series.

PubMed

Lucio, J H; Valdés, R; Rodríguez, L R

2012-05-01

The method of surrogate data has been extensively applied to hypothesis testing of system linearity, when only one realization of the system, a time series, is known. Normally, surrogate data should preserve the linear stochastic structure and the amplitude distribution of the original series. Classical surrogate data methods (such as random permutation, amplitude adjusted Fourier transform, or iterative amplitude adjusted Fourier transform) are successful at preserving one or both of these features in stationary cases. However, they always produce stationary surrogates, hence existing nonstationarity could be interpreted as dynamic nonlinearity. Certain modifications have been proposed that additionally preserve some nonstationarity, at the expense of reproducing a great deal of nonlinearity. However, even those methods generally fail to preserve the trend (i.e., global nonstationarity in the mean) of the original series. This is the case of time series with unit roots in their autoregressive structure. Additionally, those methods, based on Fourier transform, either need first and last values in the original series to match, or they need to select a piece of the original series with matching ends. These conditions are often inapplicable and the resulting surrogates are adversely affected by the well-known artefact problem. In this study, we propose a simple technique that, applied within existing Fourier-transform-based methods, generates surrogate data that jointly preserve the aforementioned characteristics of the original series, including (even strong) trends. Moreover, our technique avoids the negative effects of end mismatch. Several artificial and real, stationary and nonstationary, linear and nonlinear time series are examined, in order to demonstrate the advantages of the methods. Corresponding surrogate data are produced with the classical and with the proposed methods, and the results are compared.

Ince-Gaussian series representation of the two-dimensional fractional Fourier transform.

PubMed

Bandres, Miguel A; Gutiérrez-Vega, Julio C

2005-03-01

We introduce the Ince-Gaussian series representation of the two-dimensional fractional Fourier transform in elliptical coordinates. A physical interpretation is provided in terms of field propagation in quadratic graded-index media whose eigenmodes in elliptical coordinates are derived for the first time to our knowledge. The kernel of the new series representation is expressed in terms of Ince-Gaussian functions. The equivalence among the Hermite-Gaussian, Laguerre-Gaussian, and Ince-Gaussian series representations is verified by establishing the relation among the three definitions.

Method for determining formation quality factor from seismic data

DOEpatents

Taner, M. Turhan; Treitel, Sven

2005-08-16

A method is disclosed for calculating the quality factor Q from a seismic data trace. The method includes calculating a first and a second minimum phase inverse wavelet at a first and a second time interval along the seismic data trace, synthetically dividing the first wavelet by the second wavelet, Fourier transforming the result of the synthetic division, calculating the logarithm of this quotient of Fourier transforms and determining the slope of a best fit line to the logarithm of the quotient.

Analog 65/130 nm CMOS 5 GHz Sub-Arrays with ROACH-2 FPGA Beamformers for Hybrid Aperture-Array Receivers

DTIC Science & Technology

2017-03-20

sub-array, which is based on all-pass filters (APFs) is realized using 130 nm CMOS technology. Approximate- discrete Fourier transform (a-DFT...fixed beams are directed at known directions [9]. The proposed approximate- discrete Fourier transform (a-DFT) based multi-beamformer [9] yields L...to digital conversion daughter board. occurs in the discrete time domain (in ROACH-2 FPGA platform) following signal digitization (see Figs. 1(d) and

Note: Modification of an FTIR spectrometer for optoelectronic characterizations.

PubMed

Puspitosari, N; Longeaud, C

2017-08-01

We propose a very simple system to be adapted to a Fourier Transform Infra-Red (FTIR) spectrometer with which three different types of characterizations can be done: the Fourier transform photocurrent spectroscopy, the recording of reflection-transmission spectra of thin film semiconductors, and the acquisition of spectral responses of solar cells. In addition to gather three techniques into a single apparatus, this FTIR-based system also significantly reduces the recording time and largely improves the resolution of the measured spectra compared to standard equipments.

Fourier transform spectrometry for fiber-optic sensor systems

NASA Technical Reports Server (NTRS)

Beheim, Glenn; Tuma, Margaret L.; Sotomayor, Jorge L.; Flatico, Joseph M.

1993-01-01

An integrated-optic Mach-Zehnder interferometer is used as a Fourier transform spectrometer to analyze the input and output spectra of a temperature-sensing thin-film etalon. This type of spectrometer has an advantage over conventional grating spectrometers because it is better suited for use with time-division-multiplexed sensor networks. In addition, this spectrometer has the potential for low cost due to its use of a component that could be manufactured in large quantities for the optical communications industry.

Note: Modification of an FTIR spectrometer for optoelectronic characterizations

NASA Astrophysics Data System (ADS)

Puspitosari, N.; Longeaud, C.

2017-08-01

We propose a very simple system to be adapted to a Fourier Transform Infra-Red (FTIR) spectrometer with which three different types of characterizations can be done: the Fourier transform photocurrent spectroscopy, the recording of reflection-transmission spectra of thin film semiconductors, and the acquisition of spectral responses of solar cells. In addition to gather three techniques into a single apparatus, this FTIR-based system also significantly reduces the recording time and largely improves the resolution of the measured spectra compared to standard equipments.

Optical computing using optical flip-flops in Fourier processors: use in matrix multiplication and discrete linear transforms.

PubMed

Ando, S; Sekine, S; Mita, M; Katsuo, S

1989-12-15

An architecture and the algorithms for matrix multiplication using optical flip-flops (OFFs) in optical processors are proposed based on residue arithmetic. The proposed system is capable of processing all elements of matrices in parallel utilizing the information retrieving ability of optical Fourier processors. The employment of OFFs enables bidirectional data flow leading to a simpler architecture and the burden of residue-to-decimal (or residue-to-binary) conversion to operation time can be largely reduced by processing all elements in parallel. The calculated characteristics of operation time suggest a promising use of the system in a real time 2-D linear transform.

[Study on Differential Optical Absorption Spectroscopy Data Processing Based on Chirp-Z Transformation].

PubMed

Zheng, Hai-ming; Li, Guang-jie; Wu, Hao

2015-06-01

Differential optical absorption spectroscopy (DOAS) is a commonly used atmospheric pollution monitoring method. Denoising of monitoring spectral data will improve the inversion accuracy. Fourier transform filtering method is effectively capable of filtering out the noise in the spectral data. But the algorithm itself can introduce errors. In this paper, a chirp-z transform method is put forward. By means of the local thinning of Fourier transform spectrum, it can retain the denoising effect of Fourier transform and compensate the error of the algorithm, which will further improve the inversion accuracy. The paper study on the concentration retrieving of SO2 and NO2. The results show that simple division causes bigger error and is not very stable. Chirp-z transform is proved to be more accurate than Fourier transform. Results of the frequency spectrum analysis show that Fourier transform cannot solve the distortion and weakening problems of characteristic absorption spectrum. Chirp-z transform shows ability in fine refactoring of specific frequency spectrum.

Fourier removal of stripe artifacts in IRAS images

NASA Technical Reports Server (NTRS)

Van Buren, Dave

1987-01-01

By working in the Fourier plane, approximate removal of stripe artifacts in IRAS images can be effected. The image of interest is smoothed and subtracted from the original, giving the high-spatial-frequency part. This 'filtered' image is then clipped to remove point sources and then Fourier transformed. Subtracting the Fourier components contributing to the stripes in this image from the Fourier transform of the original and transforming back to the image plane yields substantial removal of the stripes.

Ambient infrared laser ablation mass spectrometry (AIRLAB-MS) with plume capture by continuous flow solvent probe

DOEpatents

O'Brien, Jeremy T.; Williams, Evan R.; Holman, Hoi-Ying N.

2017-10-31

A new experimental setup for spatially resolved ambient infrared laser ablation mass spectrometry (AIRLAB-MS) that uses an infrared microscope with an infinity-corrected reflective objective and a continuous flow solvent probe coupled to a Fourier transform ion cyclotron resonance mass spectrometer is described. The efficiency of material transfer from the sample to the electrospray ionization emitter was determined using glycerol/methanol droplets containing 1 mM nicotine and is .about.50%. This transfer efficiency is significantly higher than values reported for similar techniques.

Vibrations Detection in Industrial Pumps Based on Spectral Analysis to Increase Their Efficiency

NASA Astrophysics Data System (ADS)

Rachid, Belhadef; Hafaifa, Ahmed; Boumehraz, Mohamed

2016-03-01

Spectral analysis is the key tool for the study of vibration signals in rotating machinery. In this work, the vibration analysis applied for conditional preventive maintenance of such machines is proposed, as part of resolved problems related to vibration detection on the organs of these machines. The vibration signal of a centrifugal pump was treated to mount the benefits of the approach proposed. The obtained results present the signal estimation of a pump vibration using Fourier transform technique compared by the spectral analysis methods based on Prony approach.

Fourier transform imaging of impurities in the unit cells of crystals: Mn in GaAs

NASA Astrophysics Data System (ADS)

Lee, T.-L.; Bihler, C.; Schoch, W.; Limmer, W.; Daeubler, J.; Thieß, S.; Brandt, M. S.; Zegenhagen, J.

2010-06-01

The lattice sites of Mn in ferromagnetic (Ga,Mn)As thin films were imaged using the x-ray standing wave technique. The model-free images, obtained straightforwardly by Fourier inversion, disclose immediately that the Mn mostly substitutes the Ga with a small fraction residing on minority sites. The images further reveal variations in the Mn concentrations of the different sites upon post-growth treatments. Subsequent model refinement based on the directly reconstructed images resolves with high precision the complete Mn site distributions. It is found that post-growth annealing increases the fraction of substitutional Mn at the expense of interstitial Mn whereas hydrogenation has little influence on the Mn site distribution. Our study offers an element-specific high-resolution imaging approach for accurately determining the detailed site distributions of dilute concentrations of atoms in crystals.

Partial differential equation transform — Variational formulation and Fourier analysis

PubMed Central

Wang, Yang; Wei, Guo-Wei; Yang, Siyang

2011-01-01

Nonlinear partial differential equation (PDE) models are established approaches for image/signal processing, data analysis and surface construction. Most previous geometric PDEs are utilized as low-pass filters which give rise to image trend information. In an earlier work, we introduced mode decomposition evolution equations (MoDEEs), which behave like high-pass filters and are able to systematically provide intrinsic mode functions (IMFs) of signals and images. Due to their tunable time-frequency localization and perfect reconstruction, the operation of MoDEEs is called a PDE transform. By appropriate selection of PDE transform parameters, we can tune IMFs into trends, edges, textures, noise etc., which can be further utilized in the secondary processing for various purposes. This work introduces the variational formulation, performs the Fourier analysis, and conducts biomedical and biological applications of the proposed PDE transform. The variational formulation offers an algorithm to incorporate two image functions and two sets of low-pass PDE operators in the total energy functional. Two low-pass PDE operators have different signs, leading to energy disparity, while a coupling term, acting as a relative fidelity of two image functions, is introduced to reduce the disparity of two energy components. We construct variational PDE transforms by using Euler-Lagrange equation and artificial time propagation. Fourier analysis of a simplified PDE transform is presented to shed light on the filter properties of high order PDE transforms. Such an analysis also offers insight on the parameter selection of the PDE transform. The proposed PDE transform algorithm is validated by numerous benchmark tests. In one selected challenging example, we illustrate the ability of PDE transform to separate two adjacent frequencies of sin(x) and sin(1.1x). Such an ability is due to PDE transform’s controllable frequency localization obtained by adjusting the order of PDEs. The frequency selection is achieved either by diffusion coefficients or by propagation time. Finally, we explore a large number of practical applications to further demonstrate the utility of proposed PDE transform. PMID:22207904

2D non-separable linear canonical transform (2D-NS-LCT) based cryptography

NASA Astrophysics Data System (ADS)

Zhao, Liang; Muniraj, Inbarasan; Healy, John J.; Malallah, Ra'ed; Cui, Xiao-Guang; Ryle, James P.; Sheridan, John T.

2017-05-01

The 2D non-separable linear canonical transform (2D-NS-LCT) can describe a variety of paraxial optical systems. Digital algorithms to numerically evaluate the 2D-NS-LCTs are not only important in modeling the light field propagations but also of interest in various signal processing based applications, for instance optical encryption. Therefore, in this paper, for the first time, a 2D-NS-LCT based optical Double-random- Phase-Encryption (DRPE) system is proposed which offers encrypting information in multiple degrees of freedom. Compared with the traditional systems, i.e. (i) Fourier transform (FT); (ii) Fresnel transform (FST); (iii) Fractional Fourier transform (FRT); and (iv) Linear Canonical transform (LCT), based DRPE systems, the proposed system is more secure and robust as it encrypts the data with more degrees of freedom with an augmented key-space.

Spectral analysis comparisons of Fourier-theory-based methods and minimum variance (Capon) methods

NASA Astrophysics Data System (ADS)

Garbanzo-Salas, Marcial; Hocking, Wayne. K.

2015-09-01

In recent years, adaptive (data dependent) methods have been introduced into many areas where Fourier spectral analysis has traditionally been used. Although the data-dependent methods are often advanced as being superior to Fourier methods, they do require some finesse in choosing the order of the relevant filters. In performing comparisons, we have found some concerns about the mappings, particularly when related to cases involving many spectral lines or even continuous spectral signals. Using numerical simulations, several comparisons between Fourier transform procedures and minimum variance method (MVM) have been performed. For multiple frequency signals, the MVM resolves most of the frequency content only for filters that have more degrees of freedom than the number of distinct spectral lines in the signal. In the case of Gaussian spectral approximation, MVM will always underestimate the width, and can misappropriate the location of spectral line in some circumstances. Large filters can be used to improve results with multiple frequency signals, but are computationally inefficient. Significant biases can occur when using MVM to study spectral information or echo power from the atmosphere. Artifacts and artificial narrowing of turbulent layers is one such impact.

High-resolution Fourier transform synchrotron spectroscopy of the C-S stretching band of methyl mercaptan, CH332SH

NASA Astrophysics Data System (ADS)

Lees, R. M.; Xu, Li-Hong; Billinghurst, B. E.

2016-01-01

The C-S stretching fundamental band of 12CH332SH, the principal isotopologue of methyl mercaptan, has been investigated by Fourier transform infrared spectroscopy on the Far-Infrared beamline at the Canadian Light Source synchrotron. The band is centered around 710 cm-1 and shows well-resolved a-type parallel structure. Most of the A and E spectral sub-bands have been assigned up to K = 12 for the vt = 0 torsional state and K = 9 for the vt = 1 state, along with a smaller variety of sub-bands for vt = 2. C-S stretching energy term values have been determined employing known ground-state energies, and have been fitted to series expansions in powers of J(J + 1) to determine the substate origins. The origins have in turn been fitted to a Fourier model to characterize the oscillatory torsional energy structure of the C-S stretching state. The amplitude of oscillation of the vt = 0 torsional curves is significantly larger for the C-S stretch state compared to the ground state. A strategy devised to relate this amplitude to an effective torsional barrier height indicates a decrease of about 7% in the effective V3 for the C-S stretch. The vibrational frequency determined for the stretching fundamental from the Fourier fit is 710.3 cm-1. The C-S stretching manifold is crossed by excited vt = 4 torsional levels of the ground state, and strong torsion-vibrational resonant coupling is observed via perturbations in the spectrum together with forbidden sub-bands induced by mixing and intensity borrowing.

Optical Frequency Comb Fourier Transform Spectroscopy with Resolution Exceeding the Limit Set by the Optical Path Difference

NASA Astrophysics Data System (ADS)

Foltynowicz, Aleksandra; Rutkowski, Lucile; Johanssson, Alexandra C.; Khodabakhsh, Amir; Maslowski, Piotr; Kowzan, Grzegorz; Lee, Kevin; Fermann, Martin

2015-06-01

Fourier transform spectrometers (FTS) based on optical frequency combs (OFC) allow detection of broadband molecular spectra with high signal-to-noise ratios within acquisition times orders of magnitude shorter than traditional FTIRs based on thermal sources. Due to the pulsed nature of OFCs the interferogram consists of a series of bursts rather than a single burst at zero optical path difference (OPD). The comb mode structure can be resolved by acquiring multiple bursts, in both mechanical FTS systems and dual-comb spectroscopy. However, in all existing demonstrations the resolution was ultimately limited either by the maximum available OPD between the interferometer arms or by the total acquisition time enabled by the storage memory. We present a method that provides spectral resolution exceeding the limit set by the maximum OPD using an interferogram containing only a single burst. The method allows measurements of absorption lines narrower than the OPD-limited resolution without any influence of the instrumental lineshape function. We demonstrate this by measuring undistorted CO2 and CO absorption lines with linewidth narrower than the OPD-limited resolution using OFC-based mechanical FTS in the near- and mid-infrared wavelength ranges. The near-infrared system is based on an Er:fiber femtosecond laser locked to a high finesse cavity, while the mid-infrared system is based on a Tm:fiber-laser-pumped optical parametric oscillator coupled to a multi-pass cell. We show that the method allows acquisition of high-resolution molecular spectra with interferometer length orders of magnitude shorter than traditional FTIR. Mandon, J., G. Guelachvili, and N. Picque, Nat. Phot., 2009. 3(2): p. 99-102. Zeitouny, M., et al., Ann. Phys., 2013. 525(6): p. 437-442. Zolot, A.M., et al., Opt. Lett., 2012. 37(4): p. 638-640.

Polarized reflectance and transmittance properties of windblown sea surfaces.

PubMed

Mobley, Curtis D

2015-05-20

Generation of random sea surfaces using wave variance spectra and Fourier transforms is formulated in a way that guarantees conservation of wave energy and fully resolves wave height and slope variances. Monte Carlo polarized ray tracing, which accounts for multiple scattering between light rays and wave facets, is used to compute effective Mueller matrices for reflection and transmission of air- or water-incident polarized radiance. Irradiance reflectances computed using a Rayleigh sky radiance distribution, sea surfaces generated with Cox-Munk statistics, and unpolarized ray tracing differ by 10%-18% compared with values computed using elevation- and slope-resolving surfaces and polarized ray tracing. Radiance reflectance factors, as used to estimate water-leaving radiance from measured upwelling and sky radiances, are shown to depend on sky polarization, and improved values are given.

Recent applications of hyperspectral imaging in microbiology.

PubMed

Gowen, Aoife A; Feng, Yaoze; Gaston, Edurne; Valdramidis, Vasilis

2015-05-01

Hyperspectral chemical imaging (HSI) is a broad term encompassing spatially resolved spectral data obtained through a variety of modalities (e.g. Raman scattering, Fourier transform infrared microscopy, fluorescence and near-infrared chemical imaging). It goes beyond the capabilities of conventional imaging and spectroscopy by obtaining spatially resolved spectra from objects at spatial resolutions varying from the level of single cells up to macroscopic objects (e.g. foods). In tandem with recent developments in instrumentation and sampling protocols, applications of HSI in microbiology have increased rapidly. This article gives a brief overview of the fundamentals of HSI and a comprehensive review of applications of HSI in microbiology over the past 10 years. Technical challenges and future perspectives for these techniques are also discussed. Copyright © 2015 Elsevier B.V. All rights reserved.

Improvement of depth resolution in depth-resolved wavenumber-scanning interferometry using wavenumber-domain least-squares algorithm: comparison and experiment.

PubMed

Bai, Yulei; Jia, Quanjie; Zhang, Yun; Huang, Qiquan; Yang, Qiyu; Ye, Shuangli; He, Zhaoshui; Zhou, Yanzhou; Xie, Shengli

2016-05-01

It is important to improve the depth resolution in depth-resolved wavenumber-scanning interferometry (DRWSI) owing to the limited range of wavenumber scanning. In this work, a new nonlinear iterative least-squares algorithm called the wavenumber-domain least-squares algorithm (WLSA) is proposed for evaluating the phase of DRWSI. The simulated and experimental results of the Fourier transform (FT), complex-number least-squares algorithm (CNLSA), eigenvalue-decomposition and least-squares algorithm (EDLSA), and WLSA were compared and analyzed. According to the results, the WLSA is less dependent on the initial values, and the depth resolution δz is approximately changed from δz to δz/6. Thus, the WLSA exhibits a better performance than the FT, CNLSA, and EDLSA.

Immittance Data Validation by Kramers‐Kronig Relations – Derivation and Implications

PubMed Central

2017-01-01

Abstract Explicitly based on causality, linearity (superposition) and stability (time invariance) and implicit on continuity (consistency), finiteness (convergence) and uniqueness (single valuedness) in the time domain, Kramers‐Kronig (KK) integral transform (KKT) relations for immittances are derived as pure mathematical constructs in the complex frequency domain using the two‐sided (bilateral) Laplace integral transform (LT) reduced to the Fourier domain for sufficiently rapid exponential decaying, bounded immittances. Novel anti KK relations are also derived to distinguish LTI (linear, time invariant) systems from non‐linear, unstable and acausal systems. All relations can be used to test KK transformability on the LTI principles of linearity, stability and causality of measured and model data by Fourier transform (FT) in immittance spectroscopy (IS). Also, integral transform relations are provided to estimate (conjugate) immittances at zero and infinite frequency particularly useful to normalise data and compare data. Also, important implications for IS are presented and suggestions for consistent data analysis are made which generally apply likewise to complex valued quantities in many fields of engineering and natural sciences. PMID:29577007

Observation of CO 2 in Fourier transform infrared spectral measurements of living Acholeplasma laidlawii cells

NASA Astrophysics Data System (ADS)

Omura, Yoko; Okazaki, Norio

2003-06-01

In monitoring the time course of conformational disorder by Fourier transform infrared spectroscopy for intact Acholeplasma laidlawii cells grown at 37 °C on binary fatty acid mixtures containing oleic acid and for cells grown on pure palmitic acid, an absorption band at 2343 cm-1 was observed. The band intensity was found to increase with time. This band was not observed in the spectra for isolated membranes. It is suggested that the 2343 cm-1 band is due to CO2 dissolved in water, most likely produced at the final point of fermentation of amino acid by this microorganism.

A Photoluminescence Study of the Changes Induced in the Zinc White Pigment by Formation of Zinc Complexes

PubMed Central

Artesani, Alessia; Gherardi, Francesca; Nevin, Austin; Valentini, Gianluca; Comelli, Daniela

2017-01-01

It is known that oil paintings containing zinc white are subject to rapid degradation. This is caused by the interaction between the active groups of binder and the metal ions of the pigment, which gives rise to the formation of new zinc complexes (metal soaps). Ongoing studies on zinc white paints have been limited to the chemical mechanisms that lead to the formation of zinc complexes. On the contrary, little is known of the photo-physical changes induced in the zinc oxide crystal structure following this interaction. Time-resolved photoluminescence spectroscopy has been applied to follow modifications in the luminescent zinc white pigment when mixed with binder. Significant changes in trap state photoluminescence emissions have been detected: the enhancement of a blue emission combined with a change of the decay kinetic of the well-known green emission. Complementary data from molecular analysis of paints using Fourier transform infrared spectroscopy confirms the formation of zinc carboxylates and corroborates the mechanism for zinc complexes formation. We support the hypothesis that zinc ions migrate into binder creating novel vacancies, affecting the photoluminescence intensity and lifetime properties of zinc oxide. Here, we further demonstrate the advantages of a time-resolved photoluminescence approach for studying defects in semiconductor pigments. PMID:28772700

EM Propagation & Atmospheric Effects Assessment

DTIC Science & Technology

2008-09-30

The split-step Fourier parabolic equation ( SSPE ) algorithm provides the complex amplitude and phase (group delay) of the continuous wave (CW) signal...the APM is based on the SSPE , we are implementing the more efficient Fourier synthesis technique to determine the transfer function. To this end a...needed in order to sample H(f) via the SSPE , and indeed with the proper parameters chosen, the two pulses can be resolved in the time window shown in

Determination of layer ordering using sliding-window Fourier transform of x-ray reflectivity data

NASA Astrophysics Data System (ADS)

Smigiel, E.; Knoll, A.; Broll, N.; Cornet, A.

1998-01-01

X-ray reflectometry allows the determination of the thickness, density and roughness of thin layers on a substrate from several Angstroms to some hundred nanometres. The thickness is determined by simulation with trial-and-error methods after extracting initial values of the layer thicknesses from the result of a classical Fast Fourier Transform (FFT) of the reflectivity data. However, the order information of the layers is lost during classical FFT. The order of the layers has then to be known a priori. In this paper, it will be shown that the order of the layers can be obtained by a sliding-window Fourier transform, the so-called Gabor representation. This joint time-frequency analysis allows the direct determination of the order of the layers and, therefore, the use of a more appropriate starting model for refining simulations. A simulated and a measured example show the interest of this method.

Geometric interpretations of the Discrete Fourier Transform (DFT)

NASA Technical Reports Server (NTRS)

Campbell, C. W.

1984-01-01

One, two, and three dimensional Discrete Fourier Transforms (DFT) and geometric interpretations of their periodicities are presented. These operators are examined for their relationship with the two sided, continuous Fourier transform. Discrete or continuous transforms of real functions have certain symmetry properties. The symmetries are examined for the one, two, and three dimensional cases. Extension to higher dimension is straight forward.

Implementation of a direct-imaging and FX correlator for the BEST-2 array

NASA Astrophysics Data System (ADS)

Foster, G.; Hickish, J.; Magro, A.; Price, D.; Zarb Adami, K.

2014-04-01

A new digital backend has been developed for the Basic Element for SKA Training II (BEST-2) array at Radiotelescopi di Medicina, INAF-IRA, Italy, which allows concurrent operation of an FX correlator, and a direct-imaging correlator and beamformer. This backend serves as a platform for testing some of the spatial Fourier transform concepts which have been proposed for use in computing correlations on regularly gridded arrays. While spatial Fourier transform-based beamformers have been implemented previously, this is, to our knowledge, the first time a direct-imaging correlator has been deployed on a radio astronomy array. Concurrent observations with the FX and direct-imaging correlator allow for direct comparison between the two architectures. Additionally, we show the potential of the direct-imaging correlator for time-domain astronomy, by passing a subset of beams though a pulsar and transient detection pipeline. These results provide a timely verification for spatial Fourier transform-based instruments that are currently in commissioning. These instruments aim to detect highly redshifted hydrogen from the epoch of reionization and/or to perform wide-field surveys for time-domain studies of the radio sky. We experimentally show the direct-imaging correlator architecture to be a viable solution for correlation and beamforming.

Local Complex Potential Based Time Dependent Wave Packet Approach to Calculation of Vibrational Excitation Cross-sections in e-N2, e-H2 and e-CO Scattering

NASA Astrophysics Data System (ADS)

Sarma, Manabendra; Singh, Raman K.; Mishra, Manoj K.

2007-12-01

Vibrational excitation cross-sections σn←m(E) in resonant e-N2, e-CO and e-H2 scattering are calculated from transition matrix elements Tn←m(E) obtained using Fourier transform of the cross correlation function <φn(R)|ψm(R,t)> where ψm(R,t); e-iHA-(R)t/ℏφm(R). Time evolution under the influence of the resonance anionic Hamiltonian HA-(A- = N2-/CO/H2-) is effected using Lanczos and fast Fourier transforms and the target (A) vibrational eigenfunctions φm(R) and φn(R) are calculated using Fourier grid Hamiltonian method applied to PE curve of the neutral target. The resulting vibrational excitation cross-section profiles provide reasonable agreement with experimental results and the cross correlation functions offer an unequivocal differentiation between the boomerang and impulse models.

Fourier Transforms for Chemists Part III. Fourier Transforms in Data Treatment.

ERIC Educational Resources Information Center

Glasser, L.

1987-01-01

Discusses the factors affecting the behavior of a spectral function. Lists some important properties of Fourier transform (FT) pairs that are helpful when using the FT. Notes that these properties of the mathematical formulation have identical counterparts in the physical behavior of FT systems. (TW)

Determination of Fourier Transforms on an Instructional Analog Computer

ERIC Educational Resources Information Center

Anderson, Owen T.; Greenwood, Stephen R.

1974-01-01

An analog computer program to find and display the Fourier transform of some real, even functions is described. Oscilloscope traces are shown for Fourier transforms of a rectangular pulse, a Gaussian, a cosine wave, and a delayed narrow pulse. Instructional uses of the program are discussed briefly. (DT)

The application and improvement of Fourier transform spectrometer experiment

NASA Astrophysics Data System (ADS)

Liu, Zhi-min; Gao, En-duo; Zhou, Feng-qi; Wang, Lan-lan; Feng, Xiao-hua; Qi, Jin-quan; Ji, Cheng; Wang, Luning

2017-08-01

According to teaching and experimental requirements of Optoelectronic information science and Engineering, in order to consolidate theoretical knowledge and improve the students practical ability, the Fourier transform spectrometer ( FTS) experiment, its design, application and improvement are discussed in this paper. The measurement principle and instrument structure of Fourier transform spectrometer are introduced, and the spectrums of several common Laser devices are measured. Based on the analysis of spectrum and test, several possible improvement methods are proposed. It also helps students to understand the application of Fourier transform in physics.

Validating data analysis of broadband laser ranging

NASA Astrophysics Data System (ADS)

Rhodes, M.; Catenacci, J.; Howard, M.; La Lone, B.; Kostinski, N.; Perry, D.; Bennett, C.; Patterson, J.

2018-03-01

Broadband laser ranging combines spectral interferometry and a dispersive Fourier transform to achieve high-repetition-rate measurements of the position of a moving surface. Telecommunications fiber is a convenient tool for generating the large linear dispersions required for a dispersive Fourier transform, but standard fiber also has higher-order dispersion that distorts the Fourier transform. Imperfections in the dispersive Fourier transform significantly complicate the ranging signal and must be dealt with to make high-precision measurements. We describe in detail an analysis process for interpreting ranging data when standard telecommunications fiber is used to perform an imperfect dispersive Fourier transform. This analysis process is experimentally validated over a 27-cm scan of static positions, showing an accuracy of 50 μm and a root-mean-square precision of 4.7 μm.

The morphing of geographical features by Fourier transformation.

PubMed

Li, Jingzhong; Liu, Pengcheng; Yu, Wenhao; Cheng, Xiaoqiang

2018-01-01

This paper presents a morphing model of vector geographical data based on Fourier transformation. This model involves three main steps. They are conversion from vector data to Fourier series, generation of intermediate function by combination of the two Fourier series concerning a large scale and a small scale, and reverse conversion from combination function to vector data. By mirror processing, the model can also be used for morphing of linear features. Experimental results show that this method is sensitive to scale variations and it can be used for vector map features' continuous scale transformation. The efficiency of this model is linearly related to the point number of shape boundary and the interceptive value n of Fourier expansion. The effect of morphing by Fourier transformation is plausible and the efficiency of the algorithm is acceptable.

Spectral estimation—What is new? What is next?

NASA Astrophysics Data System (ADS)

Tary, Jean Baptiste; Herrera, Roberto Henry; Han, Jiajun; van der Baan, Mirko

2014-12-01

Spectral estimation, and corresponding time-frequency representation for nonstationary signals, is a cornerstone in geophysical signal processing and interpretation. The last 10-15 years have seen the development of many new high-resolution decompositions that are often fundamentally different from Fourier and wavelet transforms. These conventional techniques, like the short-time Fourier transform and the continuous wavelet transform, show some limitations in terms of resolution (localization) due to the trade-off between time and frequency localizations and smearing due to the finite size of the time series of their template. Well-known techniques, like autoregressive methods and basis pursuit, and recently developed techniques, such as empirical mode decomposition and the synchrosqueezing transform, can achieve higher time-frequency localization due to reduced spectral smearing and leakage. We first review the theory of various established and novel techniques, pointing out their assumptions, adaptability, and expected time-frequency localization. We illustrate their performances on a provided collection of benchmark signals, including a laughing voice, a volcano tremor, a microseismic event, and a global earthquake, with the intention to provide a fair comparison of the pros and cons of each method. Finally, their outcomes are discussed and possible avenues for improvements are proposed.

Dynamic Time-Resolved Chirped-Pulse Rotational Spectroscopy of Vinyl Cyanide Photoproducts in a Room Temperature Flow Reactor

NASA Astrophysics Data System (ADS)

Zaleski, Daniel P.; Prozument, Kirill

2017-06-01

Chirped-pulsed (CP) Fourier transform rotational spectroscopy invented by Brooks Pate and coworkers a decade ago is an attractive tool for gas phase chemical dynamics and kinetics studies. A good reactor for such a purpose would have well-defined (and variable) temperature and pressure conditions to be amenable to accurate kinetic modeling. Furthermore, in low pressure samples with large enough number of molecular emitters, reaction dynamics can be observable directly, rather than mediated by supersonic expansion. In the present work, we are evaluating feasibility of in situ time-resolved CP spectroscopy in a room temperature flow tube reactor. Vinyl cyanide (CH_2CHCN), neat or mixed with inert gasses, flows through the reactor at pressures 1-50 μbar (0.76-38 mTorr) where it is photodissociated by a 193 nm laser. Millimeter-wave beam of the CP spectrometer co-propagates with the laser beam along the reactor tube and interacts with nascent photoproducts. Rotational transitions of HCN, HNC, and HCCCN are detected, with ≥10 μs time-steps for 500 ms following photolysis of CH_2CHCN. The post-photolysis evolution of the photoproducts' rotational line intensities is investigated for the effects of rotational and vibrational thermalization of energized photoproducts. Possible contributions from bimolecular and wall-mediated chemistry are evaluated as well.

Fast Implicit Methods For Elliptic Moving Interface Problems

DTIC Science & Technology

2015-12-11

analyzed, and tested for the Fourier transform of piecewise polynomials given on d-dimensional simplices in D-dimensional Euclidean space. These transforms...evaluation, and one to three orders of magnitude slower than the classical uniform Fast Fourier Transform. Second, bilinear quadratures ---which...a fast algorithm was derived, analyzed, and tested for the Fourier transform of pi ecewise polynomials given on d-dimensional simplices in D

The scale of the Fourier transform: a point of view of the fractional Fourier transform

NASA Astrophysics Data System (ADS)

Jimenez, C. J.; Vilardy, J. M.; Salinas, S.; Mattos, L.; Torres, C. O.

2017-01-01

In this paper using the Fourier transform of order fractional, the ray transfer matrix for the symmetrical optical systems type ABCD and the formulae by Collins for the diffraction, we obtain explicitly the expression for scaled Fourier transform conventional; this result is the great importance in optical signal processing because it offers the possibility of scaling the size of output the Fourier distribution of the system, only by manipulating the distance of the diffraction object toward the thin lens, this research also emphasizes on practical limits when a finite spherical converging lens aperture is used. Digital simulation was carried out using the numerical platform of Matlab 7.1.

Improved digital filters for evaluating Fourier and Hankel transform integrals

USGS Publications Warehouse

Anderson, Walter L.

1975-01-01

New algorithms are described for evaluating Fourier (cosine, sine) and Hankel (J0,J1) transform integrals by means of digital filters. The filters have been designed with extended lengths so that a variable convolution operation can be applied to a large class of integral transforms having the same system transfer function. A f' lagged-convolution method is also presented to significantly decrease the computation time when computing a series of like-transforms over a parameter set spaced the same as the filters. Accuracy of the new filters is comparable to Gaussian integration, provided moderate parameter ranges and well-behaved kernel functions are used. A collection of Fortran IV subprograms is included for both real and complex functions for each filter type. The algorithms have been successfully used in geophysical applications containing a wide variety of integral transforms

An Efficient Pipeline Wavefront Phase Recovery for the CAFADIS Camera for Extremely Large Telescopes

PubMed Central

Magdaleno, Eduardo; Rodríguez, Manuel; Rodríguez-Ramos, José Manuel

2010-01-01

In this paper we show a fast, specialized hardware implementation of the wavefront phase recovery algorithm using the CAFADIS camera. The CAFADIS camera is a new plenoptic sensor patented by the Universidad de La Laguna (Canary Islands, Spain): international patent PCT/ES2007/000046 (WIPO publication number WO/2007/082975). It can simultaneously measure the wavefront phase and the distance to the light source in a real-time process. The pipeline algorithm is implemented using Field Programmable Gate Arrays (FPGA). These devices present architecture capable of handling the sensor output stream using a massively parallel approach and they are efficient enough to resolve several Adaptive Optics (AO) problems in Extremely Large Telescopes (ELTs) in terms of processing time requirements. The FPGA implementation of the wavefront phase recovery algorithm using the CAFADIS camera is based on the very fast computation of two dimensional fast Fourier Transforms (FFTs). Thus we have carried out a comparison between our very novel FPGA 2D-FFTa and other implementations. PMID:22315523

An efficient pipeline wavefront phase recovery for the CAFADIS camera for extremely large telescopes.

PubMed

Magdaleno, Eduardo; Rodríguez, Manuel; Rodríguez-Ramos, José Manuel

2010-01-01

In this paper we show a fast, specialized hardware implementation of the wavefront phase recovery algorithm using the CAFADIS camera. The CAFADIS camera is a new plenoptic sensor patented by the Universidad de La Laguna (Canary Islands, Spain): international patent PCT/ES2007/000046 (WIPO publication number WO/2007/082975). It can simultaneously measure the wavefront phase and the distance to the light source in a real-time process. The pipeline algorithm is implemented using Field Programmable Gate Arrays (FPGA). These devices present architecture capable of handling the sensor output stream using a massively parallel approach and they are efficient enough to resolve several Adaptive Optics (AO) problems in Extremely Large Telescopes (ELTs) in terms of processing time requirements. The FPGA implementation of the wavefront phase recovery algorithm using the CAFADIS camera is based on the very fast computation of two dimensional fast Fourier Transforms (FFTs). Thus we have carried out a comparison between our very novel FPGA 2D-FFTa and other implementations.

Single photon detection and signal analysis for high sensitivity dosimetry based on optically stimulated luminescence with beryllium oxide

NASA Astrophysics Data System (ADS)

Radtke, J.; Sponner, J.; Jakobi, C.; Schneider, J.; Sommer, M.; Teichmann, T.; Ullrich, W.; Henniger, J.; Kormoll, T.

2018-01-01

Single photon detection applied to optically stimulated luminescence (OSL) dosimetry is a promising approach due to the low level of luminescence light and the known statistical behavior of single photon events. Time resolved detection allows to apply a variety of different and independent data analysis methods. Furthermore, using amplitude modulated stimulation impresses time- and frequency information into the OSL light and therefore allows for additional means of analysis. Considering the impressed frequency information, data analysis by using Fourier transform algorithms or other digital filters can be used for separating the OSL signal from unwanted light or events generated by other phenomena. This potentially lowers the detection limits of low dose measurements and might improve the reproducibility and stability of obtained data. In this work, an OSL system based on a single photon detector, a fast and accurate stimulation unit and an FPGA is presented. Different analysis algorithms which are applied to the single photon data are discussed.

Method of estimating pulse response using an impedance spectrum

DOEpatents

Morrison, John L; Morrison, William H; Christophersen, Jon P; Motloch, Chester G

2014-10-21

Electrochemical Impedance Spectrum data are used to predict pulse performance of an energy storage device. The impedance spectrum may be obtained in-situ. A simulation waveform includes a pulse wave with a period greater than or equal to the lowest frequency used in the impedance measurement. Fourier series coefficients of the pulse train can be obtained. The number of harmonic constituents in the Fourier series are selected so as to appropriately resolve the response, but the maximum frequency should be less than or equal to the highest frequency used in the impedance measurement. Using a current pulse as an example, the Fourier coefficients of the pulse are multiplied by the impedance spectrum at corresponding frequencies to obtain Fourier coefficients of the voltage response to the desired pulse. The Fourier coefficients of the response are then summed and reassembled to obtain the overall time domain estimate of the voltage using the Fourier series analysis.

Simultaneous measurement of absolute strain and differential strain based on fiber Bragg grating Fabry-Perot sensor

NASA Astrophysics Data System (ADS)

Wang, Kuiru; Wang, Bo; Yan, Binbin; Sang, Xinzhu; Yuan, Jinhui; Peng, Gang-Ding

2013-10-01

We present a fiber Bragg grating Fabry-Perot (FBG-FP) sensor using the fast Fourier transform (FFT) demodulation for measuring the absolute strain and differential strain simultaneously. The amplitude and phase characteristics of Fourier transform spectrum have been studied. The relation between the amplitude of Fourier spectrum and the differential strain has been presented. We fabricate the fiber grating FP cavity sensor, and carry out the experiment on the measurement of absolute strain and differential strain. Experimental results verify the demodulation method, and show that this sensor has a good accuracy in the scope of measurement. The demodulating method can expand the number of multiplexed sensors combining with wavelength division multiplexing and time division multiplexing.

Computing Fourier integral operators with caustics

NASA Astrophysics Data System (ADS)

Caday, Peter

2016-12-01

Fourier integral operators (FIOs) have widespread applications in imaging, inverse problems, and PDEs. An implementation of a generic algorithm for computing FIOs associated with canonical graphs is presented, based on a recent paper of de Hoop et al. Given the canonical transformation and principal symbol of the operator, a preprocessing step reduces application of an FIO approximately to multiplications, pushforwards and forward and inverse discrete Fourier transforms, which can be computed in O({N}n+(n-1)/2{log}N) time for an n-dimensional FIO. The same preprocessed data also allows computation of the inverse and transpose of the FIO, with identical runtime. Examples demonstrate the algorithm’s output, and easily extendible MATLAB/C++ source code is available from the author.

Ultra High Resolution Linear Ion Trap Orbitrap Mass Spectrometer (Orbitrap Elite) Facilitates Top Down LC MS/MS and Versatile Peptide Fragmentation Modes*

PubMed Central

Michalski, Annette; Damoc, Eugen; Lange, Oliver; Denisov, Eduard; Nolting, Dirk; Müller, Mathias; Viner, Rosa; Schwartz, Jae; Remes, Philip; Belford, Michael; Dunyach, Jean-Jacques; Cox, Juergen; Horning, Stevan; Mann, Matthias; Makarov, Alexander

2012-01-01

Although only a few years old, the combination of a linear ion trap with an Orbitrap analyzer has become one of the standard mass spectrometers to characterize proteins and proteomes. Here we describe a novel version of this instrument family, the Orbitrap Elite, which is improved in three main areas. The ion transfer optics has an ion path that blocks the line of sight to achieve more robust operation. The tandem MS acquisition speed of the dual cell linear ion trap now exceeds 12 Hz. Most importantly, the resolving power of the Orbitrap analyzer has been increased twofold for the same transient length by employing a compact, high-field Orbitrap analyzer that almost doubles the observed frequencies. An enhanced Fourier Transform algorithm—incorporating phase information—further doubles the resolving power to 240,000 at m/z 400 for a 768 ms transient. For top-down experiments, we combine a survey scan with a selected ion monitoring scan of the charge state of the protein to be fragmented and with several HCD microscans. Despite the 120,000 resolving power for SIM and HCD scans, the total cycle time is within several seconds and therefore suitable for liquid chromatography tandem MS. For bottom-up proteomics, we combined survey scans at 240,000 resolving power with data-dependent collision-induced dissociation of the 20 most abundant precursors in a total cycle time of 2.5 s—increasing protein identifications in complex mixtures by about 30%. The speed of the Orbitrap Elite furthermore allows scan modes in which complementary dissociation mechanisms are routinely obtained of all fragmented peptides. PMID:22159718

Pipelined digital SAR azimuth correlator using hybrid FFT-transversal filter

NASA Technical Reports Server (NTRS)

Wu, C.; Liu, K. Y. (Inventor)

1984-01-01

A synthetic aperture radar system (SAR) having a range correlator is provided with a hybrid azimuth correlator which utilizes a block-pipe-lined fast Fourier transform (FFT). The correlator has a predetermined FFT transform size with delay elements for delaying SAR range correlated data so as to embed in the Fourier transform operation a corner-turning function as the range correlated SAR data is converted from the time domain to a frequency domain. The azimuth correlator is comprised of a transversal filter to receive the SAR data in the frequency domain, a generator for range migration compensation and azimuth reference functions, and an azimuth reference multiplier for correlation of the SAR data. Following the transversal filter is a block-pipelined inverse FFT used to restore azimuth correlated data in the frequency domain to the time domain for imaging.

Numerical conversion of transient to harmonic response functions for linear viscoelastic materials.

PubMed

Buschmann, M D

1997-02-01

Viscoelastic material behavior is often characterized using one of the three measurements: creep, stress-relaxation or dynamic sinusoidal tests. A two-stage numerical method was developed to allow representation of data from creep and stress-relaxation tests on the Fourier axis in the Laplace domain. The method assumes linear behavior and is theoretically applicable to any transient test which attains an equilibrium state. The first stage numerically resolves the Laplace integral to convert temporal stress and strain data, from creep or stress-relaxation, to the stiffness function, G(s), evaluated on the positive real axis in the Laplace domain. This numerical integration alone allows the direct comparison of data from transient experiments which attain a final equilibrium state, such as creep and stress relaxation, and allows such data to be fitted to models expressed in the Laplace domain. The second stage of this numerical procedure maps the stiffness function, G(s), from the positive real axis to the positive imaginary axis to reveal the harmonic response function, or dynamic stiffness, G(j omega). The mapping for each angular frequency, s, is accomplished by fitting a polynomial to a subset of G(s) centered around a particular value of s, substituting js for s and thereby evaluating G(j omega). This two-stage transformation circumvents previous numerical difficulties associated with obtaining Fourier transforms of the stress and strain time domain signals. The accuracy of these transforms is verified using model functions from poroelasticity, corresponding to uniaxial confined compression of an isotropic material and uniaxial unconfined compression of a transversely isotropic material. The addition of noise to the model data does not significantly deteriorate the transformed results and data points need not be equally spaced in time. To exemplify its potential utility, this two-stage transform is applied to experimental stress relaxation data to obtain the dynamic stiffness which is then compared to direct measurements of dynamic stiffness using steady-state sinusoidal tests of the same cartilage disk in confined compression. In addition to allowing calculation of the dynamic stiffness from transient tests and the direct comparison of experimental data from different tests, these numerical methods should aid in the experimental analysis of linear and nonlinear material behavior, and increase the speed of curve-fitting routines by fitting creep or stress relaxation data to models expressed in the Laplace domain.

The fast Padé transform in magnetic resonance spectroscopy for potential improvements in early cancer diagnostics

NASA Astrophysics Data System (ADS)

Belkic, Dzevad; Belkic, Karen

2005-09-01

The convergence rates of the fast Padé transform (FPT) and the fast Fourier transform (FFT) are compared. These two estimators are used to process a time-signal encoded at 4 T by means of one-dimensional magnetic resonance spectroscopy (MRS) for healthy human brain. It is found systematically that at any level of truncation of the full signal length, the clinically relevant resonances that determine concentrations of metabolites in the investigated tissue are significantly better resolved in the FPT than in the FFT. In particular, the FPT has a better resolution than the FFT for the same signal length. Moreover, the FPT can achieve the same resolution as the FFT by using twice shorter signals. Implications of these findings for two-dimensional magnetic resonance spectroscopy as well as for two- and three-dimensional magnetic resonance spectroscopic imaging are highlighted. Self-contained cross-validation of all the results from the FPT is secured by using two conceptually different, equivalent algorithms (inside and outside the unit-circle), that are both valid in the entire complex frequency plane. The difference between the results from these two variants of the FPT is indistinguishable from the background noise. This constitutes robust error analysis of proven validity. The FPT shows promise in applications of MRS for early cancer detection.

An alternative path to the boundary: The CFT as the Fourier space of AdS

NASA Astrophysics Data System (ADS)

Tolfree, Ian M.

2009-12-01

In this thesis we shed new light on the conjectured duality between an n + 1 dimensional theory of gravity in anti de Sitter space (AdS) and an n dimensional conformal field theory (CFT) by showing that the CFT can be interpreted as the Fourier space of AdS. We then make use of this to gain insight into the nature of black hole entropy. In the first part of this thesis, we give an introduction to the ideas of and review the basics of the AdS/CFT. In the next section we make use of well known integral geometry techniques to derive the Fourier transformation of a function on AdS and see it is a function with compact support on the boundary. Comparing this to the literature, we find that the Green's functions from the literature are actually the Fourier weights of the transformation and that the boundary values of fields appearing in the correspondence are the Fourier coefficients of the transformation. One is thus left to interpret the CFT as the quantized version of a classical theory in AdS and the dual operator as the Fourier coefficients. Group theoretic considerations are discussed in relation to the transformation and its potential use in constructing QCD like theories. In the last section, we then build upon this to study the BTZ black hole. Named after its authors, Banados, Teitelboim and Zanelli, the BTZ black hole is a three dimensional (two space plus one time dimension) black hole in anti de Sitter space. Following standard procedures for modifying Fourier Transformations to accommodate quotient spaces we arrive at a mapping in a black hole background consistent with known results that yields the exact micro-states of a scalar field in a black hole background. We find that the micro-states are the Fourier coefficients on the boundary, which transform under the principal series representation of SL(2, R). Using the knowledge of how to represent a bulk scalar field in the CFT, and knowing how a black hole interacts with a scalar field, we deduce the possible representations of a black hole in the CFT. We find that the black hole micro-states live on the boundary, not on the horizon, and correspond to the possible emission modes of the black hole.

Millimeter-Wave Spectroscopy for Analytical Chemistry: Thermal Evolution of Low Volatility Impurities and Detection with a Fourier Transform Molecular Rotational Resonance Spectrometer (tev Ft-Mrr

NASA Astrophysics Data System (ADS)

Harris, Brent; Fields, Shelby S.; Neill, Justin L.; Pulliam, Robin; Muckle, Matt; Pate, Brooks

2016-06-01

Recent advances in Fourier transform millimeter-wave spectroscopy techniques have renewed the application reach of molecular rotational spectroscopy for analytical chemistry. We present a sampling method for sub ppm analysis of low volatility impurities by thermal evolution from solid powders using a millimeter-wave Fourier transform molecular rotational resonance (FT-MRR) spectrometer for detection. This application of FT-MRR is relevant to the manufacturing of safe oral pharmaceuticals. Low volatility impurities can be challenging to detect at 1 ppm levels with chromatographic techniques. One such example of a potentially mutagenic impurity is acetamide (v.p. 1 Torr at 40 C, m.p. 80 C). We measured the pure reference spectrum of acetamide by flowing the sublimated vapor pressure of acetamide crystals through the FT-MRR spectrometer. The spectrometer lower detection level (LDL) for a broadband (> 20 GHz, 10 min.) spectrum is 300 nTorr, 30 pmol, or 2 ng. For a 50 mg powder, perfect sample transfer efficiency can yield a w/w % detection limit of 35 ppb. We extended the sampling method for the acetamide reference measurement to an acetaminophen sample spiked with 5000 ppm acetamide in order to test the sample transfer efficiency when liberated from an pharmaceutical powder. A spectral reference matching algorithm detected the presence of several impurities including acetaldehyde, acetic acid, and acetonitrile that evolved at the melting point of acetaminophen, demonstrating the capability of FT-MRR for identification without a routine chemical standard. The method detection limit (MDL) without further development is less than 10 ppm w/w %. Resolved FT-MRR mixture spectra will be presented with a description of sampling methods.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wolf, Steffen; Gerwert, Klaus, E-mail: gerwert@bph.rub.de; Department of Biophysics, Chinese Academy of Sciences, Max-Planck-Gesellschaft Partner Institute for Computational Biology, 320 Yue Yang Road, 200031 Shanghai

Proton conduction along protein-bound “water wires” is an essential feature in membrane proteins. Here, we analyze in detail a transient water wire, which conducts protons via a hydrophobic barrier within a membrane protein to create a proton gradient. It is formed only for a millisecond out of three water molecules distributed at inactive positions in a polar environment in the ground state. The movement into a hydrophobic environment causes characteristic shifts of the water bands reflecting their different chemical properties. These band shifts are identified by time-resolved Fourier Transform Infrared difference spectroscopy and analyzed by biomolecular Quantum Mechanical/Molecular Mechanical simulations.more » A non-hydrogen bonded (“dangling”) O–H stretching vibration band and a broad continuum absorbance caused by a combined vibration along the water wire are identified as characteristic marker bands of such water wires in a hydrophobic environment. The results provide a basic understanding of water wires in hydrophobic environments.« less

Non-Equilibrium Water-Glassy Polymer Dynamics

NASA Astrophysics Data System (ADS)

Davis, Eric; Minelli, Matteo; Baschetti, Marco; Sarti, Giulio; Elabd, Yossef

2012-02-01

For many applications (e.g., medical implants, packaging), an accurate assessment and fundamental understanding of the dynamics of water-glassy polymer interactions is of great interest. In this study, sorption and diffusion of pure water in several glassy polymers films, such as poly(styrene) (PS), poly(methyl methacrylate) (PMMA), poly(lactide) (PLA), were measured over a wide range of vapor activities and temperatures using several experimental techniques, including quartz spring microbalance (QSM), quartz crystal microbalance (QCM), and time-resolved Fourier transform infrared-attenuated total reflectance (FTIR-ATR) spectroscopy. Non-Fickian behavior (diffusion-relaxation phenomena) was observed by all three techniques, while FTIR-ATR spectroscopy also provides information about the distribution of the states of water and water transport mechanisms on a molecular-level. Specifically, the states of water are significantly different in PS compared to PMMA and PLA. Additionally, a purely predictive non-equilibrium lattice fluid (NELF) model was applied to predict the sorption isotherms of water in these glassy polymers.

Supramolecular interactions of nonsteroidal anti-inflammatory drug in nanochannels of molecular containers: a spectroscopic, thermogravimetric and microscopic investigation.

PubMed

Maity, Banibrata; Chatterjee, Aninda; Ahmed, Sayeed Ashique; Seth, Debabrata

2014-11-10

Supramolecular host-guest complexation between the nonsteroidal anti-inflammatory drug indomethacin (IMC) and molecular containers were investigated. The weakly fluorescent drug molecule becomes highly fluorescent on complexation with different molecular containers, and time-resolved fluorescence emission spectroscopy reveals that the lifetime components of IMC significantly increase in the presence of molecular containers, compared with the lifetimes in neat water. The respective solid host-guest complexes were synthesised and characterised by Fourier transform infrared and (1) H nuclear magnetic resonance spectroscopic analysis. Microscopy techniques were used to analyse modifications of the surface morphology, owing to the formation of supramolecular complexes. The effect of the molecular container on the optical properties of IMC has also been investigated to determine the effect of nanochannels of different size and structure. © 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Infrared spectral marker bands characterizing a transient water wire inside a hydrophobic membrane protein.

PubMed

Wolf, Steffen; Freier, Erik; Cui, Qiang; Gerwert, Klaus

2014-12-14

Proton conduction along protein-bound "water wires" is an essential feature in membrane proteins. Here, we analyze in detail a transient water wire, which conducts protons via a hydrophobic barrier within a membrane protein to create a proton gradient. It is formed only for a millisecond out of three water molecules distributed at inactive positions in a polar environment in the ground state. The movement into a hydrophobic environment causes characteristic shifts of the water bands reflecting their different chemical properties. These band shifts are identified by time-resolved Fourier Transform Infrared difference spectroscopy and analyzed by biomolecular Quantum Mechanical/Molecular Mechanical simulations. A non-hydrogen bonded ("dangling") O-H stretching vibration band and a broad continuum absorbance caused by a combined vibration along the water wire are identified as characteristic marker bands of such water wires in a hydrophobic environment. The results provide a basic understanding of water wires in hydrophobic environments.

Note: Photodissociation of CH3COCN at 308 nm by time-resolved Fourier-transform infrared emission spectroscopy: Is CO a primary or secondary product?

NASA Astrophysics Data System (ADS)

Tsai, Po-Yu; Lin, King-Chuen

2013-06-01

This Note aims to clarify the source of CO in photodissociation of acetyl cyanide (CH3COCN) at 308 nm. From the theoretical aspects, a new pathway via isomerization transition state (TS) at 391 ± 8 kJ/mol is found leading to the CO + CH3NC products. An amount of 60% reactant molecules at 300 K is estimated to successfully surpass the average TS barrier lying above the excitation energy by 3.5 kJ/mol. Further, a prior distribution method is conducted to characterize the vibrational energy distribution of CO on a statistical basis. The pathway to CH3NC + CO yields a vibrational branching ratio (v = 0:v = 1:v = 2:v = 3˜0.63:0.25:0.093:0.032) in excellent agreement with the observation (0.62:0.25:0.09:0.05).

Fourier transform mass spectrometry.

PubMed

Scigelova, Michaela; Hornshaw, Martin; Giannakopulos, Anastassios; Makarov, Alexander

2011-07-01

This article provides an introduction to Fourier transform-based mass spectrometry. The key performance characteristics of Fourier transform-based mass spectrometry, mass accuracy and resolution, are presented in the view of how they impact the interpretation of measurements in proteomic applications. The theory and principles of operation of two types of mass analyzer, Fourier transform ion cyclotron resonance and Orbitrap, are described. Major benefits as well as limitations of Fourier transform-based mass spectrometry technology are discussed in the context of practical sample analysis, and illustrated with examples included as figures in this text and in the accompanying slide set. Comparisons highlighting the performance differences between the two mass analyzers are made where deemed useful in assisting the user with choosing the most appropriate technology for an application. Recent developments of these high-performing mass spectrometers are mentioned to provide a future outlook.

Fourier Transform Mass Spectrometry

PubMed Central

Scigelova, Michaela; Hornshaw, Martin; Giannakopulos, Anastassios; Makarov, Alexander

2011-01-01

This article provides an introduction to Fourier transform-based mass spectrometry. The key performance characteristics of Fourier transform-based mass spectrometry, mass accuracy and resolution, are presented in the view of how they impact the interpretation of measurements in proteomic applications. The theory and principles of operation of two types of mass analyzer, Fourier transform ion cyclotron resonance and Orbitrap, are described. Major benefits as well as limitations of Fourier transform-based mass spectrometry technology are discussed in the context of practical sample analysis, and illustrated with examples included as figures in this text and in the accompanying slide set. Comparisons highlighting the performance differences between the two mass analyzers are made where deemed useful in assisting the user with choosing the most appropriate technology for an application. Recent developments of these high-performing mass spectrometers are mentioned to provide a future outlook. PMID:21742802

Properly used ''aliasing'' can give better resolution from fewer points in Fourier transform spectroscopy

NASA Astrophysics Data System (ADS)

D'Astous, Y.; Blanchard, M.

1982-05-01

In the past years, the Journal has published a number of articles1-5 devoted to the introduction of Fourier transform spectroscopy in the undergraduate labs. In most papers, the proposed experimental setup consists of a Michelson interferometer, a light source, a light detector, and a chart recorder. The student uses this setup to record an interferogram which is then Fourier transformed to obtain the spectrogram of the light source. Although attempts have been made to ease the task of performing the required Fourier transform,6 the use of computers and Cooley-Tukey's fast Fourier transform (FFT) algorithm7 is by far the simplest method to use. However, to be able to use FFT, one has to get a number of samples of the interferogram, a tedious job which should be kept to a minimum. (AIP)

The morphing of geographical features by Fourier transformation

PubMed Central

Liu, Pengcheng; Yu, Wenhao; Cheng, Xiaoqiang

2018-01-01

This paper presents a morphing model of vector geographical data based on Fourier transformation. This model involves three main steps. They are conversion from vector data to Fourier series, generation of intermediate function by combination of the two Fourier series concerning a large scale and a small scale, and reverse conversion from combination function to vector data. By mirror processing, the model can also be used for morphing of linear features. Experimental results show that this method is sensitive to scale variations and it can be used for vector map features’ continuous scale transformation. The efficiency of this model is linearly related to the point number of shape boundary and the interceptive value n of Fourier expansion. The effect of morphing by Fourier transformation is plausible and the efficiency of the algorithm is acceptable. PMID:29351344

Representation of Complex Spectra in Auditory Cortex

DTIC Science & Technology

1997-01-01

predict the response to any broadband dynamic sound. Fourier Transform Inverse Transform ∫ [.] exp(±2πjΩx±2πjwt) 2 1 2 / 1 1 a 2 1 2 / 1 1 a...Systems Research University of Maryland Spectro-Temporal Transform Ω wx = log f t w = “ripple velocity” Ω = “ripple frequency” Fourier Transform Inverse ... Transform ∫ [.] exp(±2πjΩx±2πjwt) Real functions in the spectro-temporal domain give rise to complex conjugate symmetric functions in the Fourier

Fourier transform infrared photoacoustic spectroscopy study of physicochemical interaction between human dentin and etch-&-rinse adhesives in a simulated moist bond technique.

PubMed

Ubaldini, Adriana L M; Baesso, Mauro L; Sehn, Elizandra; Sato, Francielle; Benetti, Ana R; Pascotto, Renata C

2012-06-01

The purpose of this study was to provide the physicochemical interactions at the interfaces between two commercial etch-&-rinse adhesives and human dentin in a simulated moist bond technique. Six dentin specimens were divided into two groups (n=3) according to the use of two different adhesive systems: (a) 2-hydroxyethylmethacrylate (HEMA) and 4-methacryloxyethyl trimellitate anhydrate (4-META), and (b) HEMA. The Fourier transform infrared photoacoustic spectroscopy was performed before and after dentin treatment with 37% phosphoric acid, with adhesive systems and also for the adhesive systems alone. Acid-conditioning resulted in a decalcification pattern. Adhesive treated spectra subtraction suggested the occurrence of chemical bonding to dentin expressed through modifications of the OH stretching peak (3340 cm(-1)) and symmetric CH stretching (2900 cm(-1)) for both adhesives spectra; a decrease of orthophosphate absorption band (1040 to 970 cm(-1)) for adhesive A and a better resolved complex band formation (1270 to 970 cm(-1)) for adhesive B were observed. These results suggested the occurrence of chemical bonding between sound human dentin and etch-&-rinse adhesives through a clinical typical condition.

Hyperspectral fundus imager

NASA Astrophysics Data System (ADS)

Truitt, Paul W.; Soliz, Peter; Meigs, Andrew D.; Otten, Leonard John, III

2000-11-01

A Fourier Transform hyperspectral imager was integrated onto a standard clinical fundus camera, a Zeiss FF3, for the purposes of spectrally characterizing normal anatomical and pathological features in the human ocular fundus. To develop this instrument an existing FDA approved retinal camera was selected to avoid the difficulties of obtaining new FDA approval. Because of this, several unusual design constraints were imposed on the optical configuration. Techniques to calibrate the sensor and to define where the hyperspectral pushbroom stripe was located on the retina were developed, including the manufacturing of an artificial eye with calibration features suitable for a spectral imager. In this implementation the Fourier transform hyperspectral imager can collect over a hundred 86 cm-1 spectrally resolved bands with 12 micro meter/pixel spatial resolution within the 1050 nm to 450 nm band. This equates to 2 nm to 8 nm spectral resolution depending on the wavelength. For retinal observations the band of interest tends to lie between 475 nm and 790 nm. The instrument has been in use over the last year successfully collecting hyperspectral images of the optic disc, retinal vessels, choroidal vessels, retinal backgrounds, and macula diabetic macular edema, and lesions of age-related macular degeneration.

[Optical-fiber Fourier transform spectrometer].

PubMed

Liu, Yong; Li, Bao-sheng; Liu, Yan; Zhai, Yu-feng; Wang, An

2006-10-01

A novel Fourier transform spectrum analyzer based on a single mode fiber Mach-Zehnder interferometer is reported. An optical fiber Fourier transform spectrometer, with bulk optics components replaced by fiber optical components and with the moving mirror replaced by a piezoelectric element fiber stretcher was constructed. The output spectrum of a LD below threshold was measured. Experiment result agrees with that by using grating spectrum analyzer, showing the feasibility of the optic fiber Fourier transform spectrometer for practical spectrum measurement. Spectrum resolution -7 cm(-1) was obtained in our experiment. The resolution can be further improved by increasing the maximum optical path difference.

Rotation-vibration interactions in the spectra of polycyclic aromatic hydrocarbons: Quinoline as a test-case species

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pirali, O.; Gruet, S.; Institut des Sciences Moléculaires d’Orsay, UMR8214 CNRS – Université Paris-Sud, Bât. 210, 91405 Orsay cedex

2015-03-14

Polycyclic aromatic hydrocarbons (PAHs) are highly relevant for astrophysics as possible, though controversial, carriers of the unidentified infrared emission bands that are observed in a number of different astronomical objects. In support of radio-astronomical observations, high resolution laboratory spectroscopy has already provided the rotational spectra in the vibrational ground state of several molecules of this type, although the rotational study of their dense infrared (IR) bands has only recently become possible using a limited number of experimental set-ups. To date, all of the rotationally resolved data have concerned unperturbed spectra. We presently report the results of a high resolution studymore » of the three lowest vibrational states of quinoline C{sub 9}H{sub 7}N, an N-bearing naphthalene derivative. While the pure rotational ground state spectrum of quinoline is unperturbed, severe complications appear in the spectra of the ν{sub 45} and ν{sub 44} vibrational modes (located at about 168 cm{sup −1} and 178 cm{sup −1}, respectively). In order to study these effects in detail, we employed three different and complementary experimental techniques: Fourier-transform microwave spectroscopy, millimeter-wave spectroscopy, and Fourier-transform far-infrared spectroscopy with a synchrotron radiation source. Due to the high density of states in the IR spectra of molecules as large as PAHs, perturbations in the rotational spectra of excited states should be ubiquitous. Our study identifies for the first time this effect and provides some insights into an appropriate treatment of such perturbations.« less

Trigonometric Transforms for Image Reconstruction

DTIC Science & Technology

1998-06-01

applying trigo - nometric transforms to image reconstruction problems. Many existing linear image reconstruc- tion techniques rely on knowledge of...ancestors. The research performed for this dissertation represents the first time the symmetric convolution-multiplication property of trigo - nometric...Fourier domain. The traditional representation of these filters will be similar to new trigo - nometric transform versions derived in later chapters

Automatic Fourier transform and self-Fourier beams due to parabolic potential

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhang, Yiqi, E-mail: zhangyiqi@mail.xjtu.edu.cn; Liu, Xing; Belić, Milivoj R., E-mail: milivoj.belic@qatar.tamu.edu

We investigate the propagation of light beams including Hermite–Gauss, Bessel–Gauss and finite energy Airy beams in a linear medium with parabolic potential. Expectedly, the beams undergo oscillation during propagation, but quite unexpectedly they also perform automatic Fourier transform, that is, periodic change from the beam to its Fourier transform and back. In addition to oscillation, the finite-energy Airy beams exhibit periodic inversion during propagation. The oscillating period of parity-asymmetric beams is twice that of the parity-symmetric beams. Based on the propagation in parabolic potential, we introduce a class of optically-interesting beams that are self-Fourier beams—that is, the beams whose Fouriermore » transforms are the beams themselves.« less

Holographic method for site-resolved detection of a 2D array of ultracold atoms

NASA Astrophysics Data System (ADS)

Hoffmann, Daniel Kai; Deissler, Benjamin; Limmer, Wolfgang; Hecker Denschlag, Johannes

2016-08-01

We propose a novel approach to site-resolved detection of a 2D gas of ultracold atoms in an optical lattice. A near-resonant laser beam is coherently scattered by the atomic array, and after passing a lens its interference pattern is holographically recorded by superimposing it with a reference laser beam on a CCD chip. Fourier transformation of the recorded intensity pattern reconstructs the atomic distribution in the lattice with single-site resolution. The holographic detection method requires only about two hundred scattered photons per atom in order to achieve a high reconstruction fidelity of 99.9 %. Therefore, additional cooling during detection might not be necessary even for light atomic elements such as lithium. Furthermore, first investigations suggest that small aberrations of the lens can be post-corrected in imaging processing.

Role of alloying elements on twin growth and twin transmission in magnesium alloys

DOE PAGES

Kumar, Mariyappan Arul; Beyerlein, Irene Jane; Lebensohn, Ricardo A.; ...

2017-08-24

A spatially-resolved crystal plasticity Fast Fourier Transform (FFT)-based model is employed to study the effect of alloying addition on twin thickening and twin transmission in hexagonal close packed (HCP) magnesium. In the simulations, the influence of alloying additions is represented through the differences in the critical resolved shear stress (CRSS) of different slip and twinning modes. The results show that for the same grain orientation, twin type and boundary conditions, anisotropy in the CRSS values have a significant effect on twin thickening and twin transmission. Those with large differences in CRSS favor both twin thickening and twin transmission, and vicemore » versa for those with small differences. Furthermore, less difference among the CRSS values enhances the dependence of thickening and transmission on the neighboring grain orientation.« less

A numerical resolution study of high order essentially non-oscillatory schemes applied to incompressible flow

NASA Technical Reports Server (NTRS)

Weinan, E.; Shu, Chi-Wang

1994-01-01

High order essentially non-oscillatory (ENO) schemes, originally designed for compressible flow and in general for hyperbolic conservation laws, are applied to incompressible Euler and Navier-Stokes equations with periodic boundary conditions. The projection to divergence-free velocity fields is achieved by fourth-order central differences through fast Fourier transforms (FFT) and a mild high-order filtering. The objective of this work is to assess the resolution of ENO schemes for large scale features of the flow when a coarse grid is used and small scale features of the flow, such as shears and roll-ups, are not fully resolved. It is found that high-order ENO schemes remain stable under such situations and quantities related to large scale features, such as the total circulation around the roll-up region, are adequately resolved.

A numerical resolution study of high order essentially non-oscillatory schemes applied to incompressible flow

NASA Technical Reports Server (NTRS)

Weinan, E.; Shu, Chi-Wang

1992-01-01

High order essentially non-oscillatory (ENO) schemes, originally designed for compressible flow and in general for hyperbolic conservation laws, are applied to incompressible Euler and Navier-Stokes equations with periodic boundary conditions. The projection to divergence-free velocity fields is achieved by fourth order central differences through Fast Fourier Transforms (FFT) and a mild high-order filtering. The objective of this work is to assess the resolution of ENO schemes for large scale features of the flow when a coarse grid is used and small scale features of the flow, such as shears and roll-ups, are not fully resolved. It is found that high-order ENO schemes remain stable under such situations and quantities related to large-scale features, such as the total circulation around the roll-up region, are adequately resolved.

Role of alloying elements on twin growth and twin transmission in magnesium alloys

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kumar, Mariyappan Arul; Beyerlein, Irene Jane; Lebensohn, Ricardo A.

A spatially-resolved crystal plasticity Fast Fourier Transform (FFT)-based model is employed to study the effect of alloying addition on twin thickening and twin transmission in hexagonal close packed (HCP) magnesium. In the simulations, the influence of alloying additions is represented through the differences in the critical resolved shear stress (CRSS) of different slip and twinning modes. The results show that for the same grain orientation, twin type and boundary conditions, anisotropy in the CRSS values have a significant effect on twin thickening and twin transmission. Those with large differences in CRSS favor both twin thickening and twin transmission, and vicemore » versa for those with small differences. Furthermore, less difference among the CRSS values enhances the dependence of thickening and transmission on the neighboring grain orientation.« less

Size-dependent physicochemical and mechanical interactions in battery paste anodes of Si-microwires revealed by Fast-Fourier-Transform Impedance Spectroscopy

NASA Astrophysics Data System (ADS)

Hansen, Sandra; Quiroga-González, Enrique; Carstensen, Jürgen; Adelung, Rainer; Föll, Helmut

2017-05-01

Perfectly aligned silicon microwire arrays show exceptionally high cycling stability with record setting (high) areal capacities of 4.25 mAh cm-2. Those wires have a special, modified length and thickness in order to perform this good. Geometry and sizes are the most important parameters of an anode to obtain batteries with high cycling stability without irreversible losses. The wires are prepared with a unique etching fabrication method, which allows to fabricate wires of very precise sizes. In order to investigate how good randomly oriented silicon wires perform in contrast to the perfect order of the array, the wires are embedded in a paste. This study reveals the fundamental correlation between geometry, mechanics and charge transfer kinetics of silicon electrodes. Using a suitable RC equivalent circuit allows to evaluate data from cyclic voltammetry and simultaneous FFT-Impedance Spectroscopy (FFT-IS), yielding in time-resolved resistances, time constants, and their direct correlation to the phase transformations. The change of the resistances during lithiation and delithiation correlates to kinetics and charge transfer mechanisms. This study demonstrates how the mechanical and physiochemical interactions at the silicon/paste interface inside the paste electrodes lead to void formation around silicon and with it to material loss and capacity fading.

A discrete Fourier transform for virtual memory machines

NASA Technical Reports Server (NTRS)

Galant, David C.

1992-01-01

An algebraic theory of the Discrete Fourier Transform is developed in great detail. Examination of the details of the theory leads to a computationally efficient fast Fourier transform for the use on computers with virtual memory. Such an algorithm is of great use on modern desktop machines. A FORTRAN coded version of the algorithm is given for the case when the sequence of numbers to be transformed is a power of two.

Rational Chebyshev spectral transform for the dynamics of broad-area laser diodes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Javaloyes, J., E-mail: julien.javaloyes@uib.es; Balle, S.

2015-10-01

This manuscript details the use of the rational Chebyshev transform for describing the transverse dynamics of broad-area laser diodes and amplifiers. This spectral method can be used in combination with the delay algebraic equations approach developed in [1], which substantially reduces the computation time. The theory is presented in such a way that it encompasses the case of the Fourier spectral transform presented in [2] as a particular case. It is also extended to the consideration of index guiding with an arbitrary transverse profile. Because their domain of definition is infinite, the convergence properties of the Chebyshev rational functions allowmore » handling the boundary conditions with higher accuracy than with the previously studied Fourier transform method. As practical examples, we solve the beam propagation problem with and without index guiding: we obtain excellent results and an improvement of the integration time between one and two orders of magnitude as compared with a fully distributed two dimensional model.« less

Diffractive shear interferometry for extreme ultraviolet high-resolution lensless imaging

NASA Astrophysics Data System (ADS)

Jansen, G. S. M.; de Beurs, A.; Liu, X.; Eikema, K. S. E.; Witte, S.

2018-05-01

We demonstrate a novel imaging approach and associated reconstruction algorithm for far-field coherent diffractive imaging, based on the measurement of a pair of laterally sheared diffraction patterns. The differential phase profile retrieved from such a measurement leads to improved reconstruction accuracy, increased robustness against noise, and faster convergence compared to traditional coherent diffractive imaging methods. We measure laterally sheared diffraction patterns using Fourier-transform spectroscopy with two phase-locked pulse pairs from a high harmonic source. Using this approach, we demonstrate spectrally resolved imaging at extreme ultraviolet wavelengths between 28 and 35 nm.

Absorbing metasurface created by diffractionless disordered arrays of nanoantennas

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chevalier, Paul; Minao, Laboratoire de Photonique et Nanostructures; Bouchon, Patrick, E-mail: patrick.bouchon@onera.fr

2015-12-21

We study disordered arrays of metal-insulator-metal nanoantenna in order to create a diffractionless metasurface able to absorb light in the 3–5 μm spectral range. This study is conducted with angle-resolved reflectivity measurements obtained with a Fourier transform infrared spectrometer. A first design is based on a perturbation of a periodic arrangement, leading to a significant reduction of the radiative losses. Then, a random assembly of nanoantennas is built following a Poisson-disk distribution of given density, in order to obtain a nearly perfect cluttered assembly with optical properties of a homogeneous material.

A Simple Approach to Fourier Aliasing

ERIC Educational Resources Information Center

Foadi, James

2007-01-01

In the context of discrete Fourier transforms the idea of aliasing as due to approximation errors in the integral defining Fourier coefficients is introduced and explained. This has the positive pedagogical effect of getting to the heart of sampling and the discrete Fourier transform without having to delve into effective, but otherwise long and…

A general spectral transformation simultaneously including a Fourier transformation and a Laplace transformation

NASA Technical Reports Server (NTRS)

Marko, H.

1978-01-01

A general spectral transformation is proposed and described. Its spectrum can be interpreted as a Fourier spectrum or a Laplace spectrum. The laws and functions of the method are discussed in comparison with the known transformations, and a sample application is shown.

Fourier Analysis and Structure Determination: Part I: Fourier Transforms.

ERIC Educational Resources Information Center

Chesick, John P.

1989-01-01

Provides a brief introduction with some definitions and properties of Fourier transforms. Shows relations, ways of understanding the mathematics, and applications. Notes proofs are not included but references are given. First of three part series. (MVL)

Study on sampling of continuous linear system based on generalized Fourier transform

NASA Astrophysics Data System (ADS)

Li, Huiguang

2003-09-01

In the research of signal and system, the signal's spectrum and the system's frequency characteristic can be discussed through Fourier Transform (FT) and Laplace Transform (LT). However, some singular signals such as impulse function and signum signal don't satisfy Riemann integration and Lebesgue integration. They are called generalized functions in Maths. This paper will introduce a new definition -- Generalized Fourier Transform (GFT) and will discuss generalized function, Fourier Transform and Laplace Transform under a unified frame. When the continuous linear system is sampled, this paper will propose a new method to judge whether the spectrum will overlap after generalized Fourier transform (GFT). Causal and non-causal systems are studied, and sampling method to maintain system's dynamic performance is presented. The results can be used on ordinary sampling and non-Nyquist sampling. The results also have practical meaning on research of "discretization of continuous linear system" and "non-Nyquist sampling of signal and system." Particularly, condition for ensuring controllability and observability of MIMO continuous systems in references 13 and 14 is just an applicable example of this paper.

Structure in the 3D Galaxy Distribution. III. Fourier Transforming the Universe: Phase and Power Spectra

NASA Technical Reports Server (NTRS)

Scargle, Jeffrey D.; Way, M. J.; Gazis, P. G.

2017-01-01

We demonstrate the effectiveness of a relatively straightforward analysis of the complex 3D Fourier transform of galaxy coordinates derived from redshift surveys. Numerical demonstrations of this approach are carried out on a volume-limited sample of the Sloan Digital Sky Survey redshift survey. The direct unbinned transform yields a complex 3D data cube quite similar to that from the Fast Fourier Transform of finely binned galaxy positions. In both cases, deconvolution of the sampling window function yields estimates of the true transform. Simple power spectrum estimates from these transforms are roughly consistent with those using more elaborate methods. The complex Fourier transform characterizes spatial distributional properties beyond the power spectrum in a manner different from (and we argue is more easily interpreted than) the conventional multipoint hierarchy. We identify some threads of modern large-scale inference methodology that will presumably yield detections in new wider and deeper surveys.

A fractional Fourier transform analysis of the scattering of ultrasonic waves.

PubMed

Tant, Katherine M M; Mulholland, Anthony J; Langer, Matthias; Gachagan, Anthony

2015-03-08

Many safety critical structures, such as those found in nuclear plants, oil pipelines and in the aerospace industry, rely on key components that are constructed from heterogeneous materials. Ultrasonic non-destructive testing (NDT) uses high-frequency mechanical waves to inspect these parts, ensuring they operate reliably without compromising their integrity. It is possible to employ mathematical models to develop a deeper understanding of the acquired ultrasonic data and enhance defect imaging algorithms. In this paper, a model for the scattering of ultrasonic waves by a crack is derived in the time-frequency domain. The fractional Fourier transform (FrFT) is applied to an inhomogeneous wave equation where the forcing function is prescribed as a linear chirp, modulated by a Gaussian envelope. The homogeneous solution is found via the Born approximation which encapsulates information regarding the flaw geometry. The inhomogeneous solution is obtained via the inverse Fourier transform of a Gaussian-windowed linear chirp excitation. It is observed that, although the scattering profile of the flaw does not change, it is amplified. Thus, the theory demonstrates the enhanced signal-to-noise ratio permitted by the use of coded excitation, as well as establishing a time-frequency domain framework to assist in flaw identification and classification.

A Final Approach Trajectory Model for Current Operations

NASA Technical Reports Server (NTRS)

Gong, Chester; Sadovsky, Alexander

2010-01-01

Predicting accurate trajectories with limited intent information is a challenge faced by air traffic management decision support tools in operation today. One such tool is the FAA's Terminal Proximity Alert system which is intended to assist controllers in maintaining safe separation of arrival aircraft during final approach. In an effort to improve the performance of such tools, two final approach trajectory models are proposed; one based on polynomial interpolation, the other on the Fourier transform. These models were tested against actual traffic data and used to study effects of the key final approach trajectory modeling parameters of wind, aircraft type, and weight class, on trajectory prediction accuracy. Using only the limited intent data available to today's ATM system, both the polynomial interpolation and Fourier transform models showed improved trajectory prediction accuracy over a baseline dead reckoning model. Analysis of actual arrival traffic showed that this improved trajectory prediction accuracy leads to improved inter-arrival separation prediction accuracy for longer look ahead times. The difference in mean inter-arrival separation prediction error between the Fourier transform and dead reckoning models was 0.2 nmi for a look ahead time of 120 sec, a 33 percent improvement, with a corresponding 32 percent improvement in standard deviation.

Realistic Analytical Polyhedral MRI Phantoms

PubMed Central

Ngo, Tri M.; Fung, George S. K.; Han, Shuo; Chen, Min; Prince, Jerry L.; Tsui, Benjamin M. W.; McVeigh, Elliot R.; Herzka, Daniel A.

2015-01-01

Purpose Analytical phantoms have closed form Fourier transform expressions and are used to simulate MRI acquisitions. Existing 3D analytical phantoms are unable to accurately model shapes of biomedical interest. It is demonstrated that polyhedral analytical phantoms have closed form Fourier transform expressions and can accurately represent 3D biomedical shapes. Theory The derivations of the Fourier transform of a polygon and polyhedron are presented. Methods The Fourier transform of a polyhedron was implemented and its accuracy in representing faceted and smooth surfaces was characterized. Realistic anthropomorphic polyhedral brain and torso phantoms were constructed and their use in simulated 3D/2D MRI acquisitions was described. Results Using polyhedra, the Fourier transform of faceted shapes can be computed to within machine precision. Smooth surfaces can be approximated with increasing accuracy by increasing the number of facets in the polyhedron; the additional accumulated numerical imprecision of the Fourier transform of polyhedra with many faces remained small. Simulations of 3D/2D brain and 2D torso cine acquisitions produced realistic reconstructions free of high frequency edge aliasing as compared to equivalent voxelized/rasterized phantoms. Conclusion Analytical polyhedral phantoms are easy to construct and can accurately simulate shapes of biomedical interest. PMID:26479724

A Comparison of Optical versus Hardware Fourier Transforms.

DTIC Science & Technology

1983-10-31

AD- R136 223 A COMPRISON’OF OPTICAL ERSUS HARDWARE FOURIER i/i.TRANSFORMS(U) VIRGINIA POLYTECHNIC INST AND STATE UNIV BLACKSBURG DEPT OF PHYSICS S P...transform and its inverse filtered Fourier transform obtained with the Digital Image Processing (DIP) hardware system located at the School of Aerospace...transparencies, and provided to us by Dr. Ralph G. Allen, Director of the Laser Effects Branch (Division of Radiation Sciences). The DIP system consisted of: an

Fourier analysis and signal processing by use of the Moebius inversion formula

NASA Technical Reports Server (NTRS)

Reed, Irving S.; Yu, Xiaoli; Shih, Ming-Tang; Tufts, Donald W.; Truong, T. K.

1990-01-01

A novel Fourier technique for digital signal processing is developed. This approach to Fourier analysis is based on the number-theoretic method of the Moebius inversion of series. The Fourier transform method developed is shown also to yield the convolution of two signals. A computer simulation shows that this method for finding Fourier coefficients is quite suitable for digital signal processing. It competes with the classical FFT (fast Fourier transform) approach in terms of accuracy, complexity, and speed.

Advances of a Brillouin Scattering Lidar System for the Detection of Temperature Profiles in the Ocean: Laboratory Measurements and Field Test

NASA Astrophysics Data System (ADS)

Walther, T.; Rupp, D.; Friman, S.; Trees, C.; Fournier, G.

2016-02-01

Recently we have demonstrated the feasibility of remotely measuring temperature profiles in water under a laboratory environment employing our real-time Brillouin Scattering LIDAR (BSL) system. The working principle is based on the frequency and time resolved detection of the backscattered spontaneous Brillouin signal of a short light pulse fired into the ocean. The light source consists of a frequency-doubled fiber-amplified External Cavity Diode Laser (ECDL) providing high-energy, Fourier transform-limited laser pulses in the green spectral range. The Brillouin shift is detected with high accuracy (low uncertainty) by employing an edge filter based on an Excited State Faraday Anomalous Dispersion Optical Filter (ESFADOF). Time-resolution allows for the depth resolution and the frequency resolved shift is proportional to the speed of sound. Thus, the temperature profile can be extracted from the measurements. In our laboratory setup we were able to resolve water temperatures with a mean accuracy of up to 0.07 oC and a spatial resolution of 1 m depending on the amount of averaging. In order to prepare the system for a first field test under realistic conditions on the coast of the Mediterranean at CMRE in La Spezia, almost all of the components have been upgraded. This first test is planned for November 2015. We will present the above mentioned measurements, details about the upgrades and report on our experiences during this maritime field test.Ultimately, the plan is to operate the system from a mobile platform, e.g., a helicopter or vessel, in order to precisely determine the temperature of the surface mixed layer of the ocean with high spatial resolution.

A fractional Fourier transform analysis of a bubble excited by an ultrasonic chirp.

PubMed

Barlow, Euan; Mulholland, Anthony J

2011-11-01

The fractional Fourier transform is proposed here as a model based, signal processing technique for determining the size of a bubble in a fluid. The bubble is insonified with an ultrasonic chirp and the radiated pressure field is recorded. This experimental bubble response is then compared with a series of theoretical model responses to identify the most accurate match between experiment and theory which allows the correct bubble size to be identified. The fractional Fourier transform is used to produce a more detailed description of each response, and two-dimensional cross correlation is then employed to identify the similarities between the experimental response and each theoretical response. In this paper the experimental bubble response is simulated by adding various levels of noise to the theoretical model output. The method is compared to the standard technique of using time-domain cross correlation. The proposed method is shown to be far more robust at correctly sizing the bubble and can cope with much lower signal to noise ratios.

Cheating Heisenberg: Achieving certainty in wideband spectrography

NASA Astrophysics Data System (ADS)

Fulop, Sean

2003-10-01

The spectrographic analysis of sound has been with us some 58 years, and one of the key properties of the process is the trade-off in resolution between the time and frequency dimensions in the computed graph. While spectrography has greatly advanced the development of phonetics, the uncertainty principle has always been a source of frustration to phoneticians because so many of the interesting features of speech must be observed by computing Fourier spectra over very short time frames-i.e., using a ``wideband'' spectrogram. Since the uncertainty relation between time and frequency is unbreakable, the only option for improvement is to make a new kind of spectrogram that does not graph time and frequency. An algorithm is described and demonstrated which computes a new kind of spectrogram in which Fourier transform frequency is replaced by the channelized instantaneous frequency, and time is adjusted by the local group delay. The theory behind this procedure was clarified in Nelson [J. Acoust. Soc. Am. 110, 2575-2592 (2001)]. The resulting wideband spectrograms show dramatically improved resolution of speech features, which will be demonstrated with sample figures. It is thus suggested that phoneticians should be more interested in the instantaneous frequency spectrum than in the Fourier transform.

Hilbert-Huang Transform: A Spectral Analysis Tool Applied to Sunspot Number and Total Solar Irradiance Variations, as well as Near-Surface Atmospheric Variables

NASA Astrophysics Data System (ADS)

Barnhart, B. L.; Eichinger, W. E.; Prueger, J. H.

2010-12-01

Hilbert-Huang transform (HHT) is a relatively new data analysis tool which is used to analyze nonstationary and nonlinear time series data. It consists of an algorithm, called empirical mode decomposition (EMD), which extracts the cyclic components embedded within time series data, as well as Hilbert spectral analysis (HSA) which displays the time and frequency dependent energy contributions from each component in the form of a spectrogram. The method can be considered a generalized form of Fourier analysis which can describe the intrinsic cycles of data with basis functions whose amplitudes and phases may vary with time. The HHT will be introduced and compared to current spectral analysis tools such as Fourier analysis, short-time Fourier analysis, wavelet analysis and Wigner-Ville distributions. A number of applications are also presented which demonstrate the strengths and limitations of the tool, including analyzing sunspot number variability and total solar irradiance proxies as well as global averaged temperature and carbon dioxide concentration. Also, near-surface atmospheric quantities such as temperature and wind velocity are analyzed to demonstrate the nonstationarity of the atmosphere.

Orthogonal fast spherical Bessel transform on uniform grid

NASA Astrophysics Data System (ADS)

Serov, Vladislav V.

2017-07-01

We propose an algorithm for the orthogonal fast discrete spherical Bessel transform on a uniform grid. Our approach is based upon the spherical Bessel transform factorization into the two subsequent orthogonal transforms, namely the fast Fourier transform and the orthogonal transform founded on the derivatives of the discrete Legendre orthogonal polynomials. The method utility is illustrated by its implementation for the problem of a two-atomic molecule in a time-dependent external field simulating the one utilized in the attosecond streaking technique.

Ultrafast nuclear dynamics in halomethanes studied with time-resolved Coulomb explosion imaging and channel-selective Fourier spectroscopy

NASA Astrophysics Data System (ADS)

Malakar, Y.; Kaderiya, B.; Pearson, W. L.; Ziaee, F.; Kanaka Raju, P.; Zohrabi, M.; Jensen, K.; Rajput, J.; Ben-Itzhak, I.; Rolles, D.; Rudenko, A.

2016-05-01

Halomethanes have recently attracted considerable attention since they often serve as prototype systems for laser-controlled chemistry (e.g., selective bond breaking or concerted elimination reactions), and are important molecules in atmospheric chemistry. Here we combine a femtosecond laser pump-probe setup with coincident 3D ion momentum imaging apparatus to study strong-field induced nuclear dynamics in methane and several of its halogenated derivatives (CH3 I, CH2 I2, CH2 ICl). We apply a time-resolved Coulomb explosion imaging technique to map the nuclear motion on both, bound and continuum potential surfaces, disentangle different fragmentation pathways and, for halogenated molecules, observe clear signatures of vibrational wave packets in neutral or ionized states. Channel-selective and kinetic-energy resolved Fourier analysis of these data allows for unique identification of different electronic states and vibrational modes responsible for a particular structure. Supported by the Chemical Sciences, Geosciences, and Biosciences Division, Office of Basic Energy Sciences, Office of Science, U. S. DOE. K. R. P. and W. L. P. supported by NSF Award No. IIA-143049. K.J. supported by the NSF-REU Grant No. PHYS-1461251.

A no-key-exchange secure image sharing scheme based on Shamir's three-pass cryptography protocol and the multiple-parameter fractional Fourier transform.

PubMed

Lang, Jun

2012-01-30

In this paper, we propose a novel secure image sharing scheme based on Shamir's three-pass protocol and the multiple-parameter fractional Fourier transform (MPFRFT), which can safely exchange information with no advance distribution of either secret keys or public keys between users. The image is encrypted directly by the MPFRFT spectrum without the use of phase keys, and information can be shared by transmitting the encrypted image (or message) three times between users. Numerical simulation results are given to verify the performance of the proposed algorithm.

Using the Fast Fourier Transform to Accelerate the Computational Search for RNA Conformational Switches

PubMed Central

Senter, Evan; Sheikh, Saad; Dotu, Ivan; Ponty, Yann; Clote, Peter

2012-01-01

Using complex roots of unity and the Fast Fourier Transform, we design a new thermodynamics-based algorithm, FFTbor, that computes the Boltzmann probability that secondary structures differ by base pairs from an arbitrary initial structure of a given RNA sequence. The algorithm, which runs in quartic time and quadratic space , is used to determine the correlation between kinetic folding speed and the ruggedness of the energy landscape, and to predict the location of riboswitch expression platform candidates. A web server is available at http://bioinformatics.bc.edu/clotelab/FFTbor/. PMID:23284639

A Constant Percentage Bandwidth Transform for Acoustic Signal Processing

DTIC Science & Technology

1980-01-01

t)eJwt d . 27Th (0) Equation 2.9 is not, however, the most general form for short-time Fourier synthesis, but is in fact a particular case of the...form of the analysis integral. F(Wk? t)eJwkt = f(t) * h( t)’ukt (3.4) Fourier transforming both sides of this equation (and invoking the convolution...properties. In what follows, define 38 f(t) - F(w,t) (3.24) to be an equivalent statement to equation 3.1. 3.6.1 Linearity Property If F1 w,t) and F2 (w

Epileptic seizure classification of EEG time-series using rational discrete short-time fourier transform.

PubMed

Samiee, Kaveh; Kovács, Petér; Gabbouj, Moncef

2015-02-01

A system for epileptic seizure detection in electroencephalography (EEG) is described in this paper. One of the challenges is to distinguish rhythmic discharges from nonstationary patterns occurring during seizures. The proposed approach is based on an adaptive and localized time-frequency representation of EEG signals by means of rational functions. The corresponding rational discrete short-time Fourier transform (DSTFT) is a novel feature extraction technique for epileptic EEG data. A multilayer perceptron classifier is fed by the coefficients of the rational DSTFT in order to separate seizure epochs from seizure-free epochs. The effectiveness of the proposed method is compared with several state-of-art feature extraction algorithms used in offline epileptic seizure detection. The results of the comparative evaluations show that the proposed method outperforms competing techniques in terms of classification accuracy. In addition, it provides a compact representation of EEG time-series.

Application of modern online instrumentation for chemical analysis of gas and particulate phases of exhaust at the European Commission heavy-duty vehicle emission laboratory.

PubMed

Adam, T W; Chirico, R; Clairotte, M; Elsasser, M; Manfredi, U; Martini, G; Sklorz, M; Streibel, T; Heringa, M F; Decarlo, P F; Baltensperger, U; De Santi, G; Krasenbrink, A; Zimmermann, R; Prevot, A S H; Astorga, C

2011-01-01

The European Commission recently established a novel test facility for heavy-duty vehicles to enhance more sustainable transport. The facility enables the study of energy efficiency of various fuels/scenarios as well as the chemical composition of evolved exhaust emissions. Sophisticated instrumentation for real-time analysis of the gas and particulate phases of exhaust has been implemented. Thereby, gas-phase characterization was carried out by a Fourier transform infrared spectrometer (FT-IR; carbonyls, nitrogen-containing species, small hydrocarbons) and a resonance-enhanced multiphoton ionization time-of-flight mass spectrometer (REMPI-TOFMS; monocyclic and polycyclic aromatic hydrocarbons). For analysis of the particulate phase, a high-resolution time-of-flight aerosol mass spectrometer (HR-TOF-AMS; organic matter, chloride, nitrate), a condensation particle counter (CPC; particle number), and a multiangle absorption photometer (MAAP; black carbon) were applied. In this paper, the first application of the new facility in combination with the described instruments is presented, whereby a medium-size truck was investigated by applying different driving cycles. The goal was simultaneous chemical characterization of a great variety of gaseous compounds and particulate matter in exhaust on a real-time basis. The time-resolved data allowed new approaches to view the results; for example, emission factors were normalized to time-resolved consumption of fuel and were related to emission factors evolved during high speeds. Compounds could be identified that followed the fuel consumption, others showed very different behavior. In particular, engine cold start, engine ignition (unburned fuel), and high-speed events resulted in unique emission patterns.

Hydrograph structure informed calibration in the frequency domain with time localization

NASA Astrophysics Data System (ADS)

Kumarasamy, K.; Belmont, P.

2015-12-01

Complex models with large number of parameters are commonly used to estimate sediment yields and predict changes in sediment loads as a result of changes in management or conservation practice at large watershed (>2000 km2) scales. As sediment yield is a strongly non-linear function that responds to channel (peak or mean) velocity or flow depth, it is critical to accurately represent flows. The process of calibration in such models (e.g., SWAT) generally involves the adjustment of several parameters to obtain better estimates of goodness of fit metrics such as Nash Sutcliff Efficiency (NSE). However, such indicators only provide a global view of model performance, potentially obscuring accuracy of the timing or magnitude of specific flows of interest. We describe an approach for streamflow calibration that will greatly reduce the black-box nature of calibration, when response from a parameter adjustment is not clearly known. Fourier Transform or the Short Term Fourier Transform could be used to characterize model performance in the frequency domain as well, however, the ambiguity of a Fourier transform with regards to time localization renders its implementation in a model calibration setting rather useless. Brief and sudden changes (e.g. stream flow peaks) in signals carry the most interesting information from parameter adjustments, which are completely lost in the transform without time localization. Wavelet transform captures the frequency component in the signal without compromising time and is applied to contrast changes in signal response to parameter adjustments. Here we employ the mother wavelet called the Mexican hat wavelet and apply a Continuous Wavelet Transform to understand the signal in the frequency domain. Further, with the use of the cross-wavelet spectrum we examine the relationship between the two signals (prior or post parameter adjustment) in the time-scale plane (e.g., lower scales correspond to higher frequencies). The non-stationarity of the streamflow signal does not hinder this assessment and regions of change called boundaries of influence (seasons or time when such change occurs in the hydrograph) for each parameter are delineated. In addition, we can discover the structural component of the signal (e.g., shifts or amplitude change) that has changed.

Data characteristic analysis of air conditioning load based on fast Fourier transform

NASA Astrophysics Data System (ADS)

Li, Min; Zhang, Yanchi; Xie, Da

2018-04-01

With the development of economy and the improvement of people's living standards, air conditioning equipment is more and more popular. The influence of air conditioning load for power grid is becoming more and more serious. In this context it is necessary to study the characteristics of air conditioning load. This paper analyzes the data of air conditioning power consumption in an office building. The data is used for Fast Fourier Transform by data analysis software. Then a series of maps are drawn for the transformed data. The characteristics of each map were analyzed separately. The hidden rules of these data are mined from the angle of frequency domain. And these rules are hard to find in the time domain.

Three-dimensional vector modeling and restoration of flat finite wave tank radiometric measurements

NASA Technical Reports Server (NTRS)

Truman, W. M.; Balanis, C. A.; Holmes, J. J.

1977-01-01

In this paper, a three-dimensional Fourier transform inversion method describing the interaction between water surface emitted radiation from a flat finite wave tank and antenna radiation characteristics is reported. The transform technique represents the scanning of the antenna mathematically as a correlation. Computation time is reduced by using the efficient and economical fast Fourier transform algorithm. To verify the inversion method, computations have been made and compared with known data and other available results. The technique has been used to restore data of the finite wave tank system and other available antenna temperature measurements made at the Cape Cod Canal. The restored brightness temperatures serve as better representations of the emitted radiation than the measured antenna temperatures.

A fast iterative convolution weighting approach for gridding-based direct Fourier three-dimensional reconstruction with correction for the contrast transfer function.

PubMed

Abrishami, V; Bilbao-Castro, J R; Vargas, J; Marabini, R; Carazo, J M; Sorzano, C O S

2015-10-01

We describe a fast and accurate method for the reconstruction of macromolecular complexes from a set of projections. Direct Fourier inversion (in which the Fourier Slice Theorem plays a central role) is a solution for dealing with this inverse problem. Unfortunately, the set of projections provides a non-equidistantly sampled version of the macromolecule Fourier transform in the single particle field (and, therefore, a direct Fourier inversion) may not be an optimal solution. In this paper, we introduce a gridding-based direct Fourier method for the three-dimensional reconstruction approach that uses a weighting technique to compute a uniform sampled Fourier transform. Moreover, the contrast transfer function of the microscope, which is a limiting factor in pursuing a high resolution reconstruction, is corrected by the algorithm. Parallelization of this algorithm, both on threads and on multiple CPU's, makes the process of three-dimensional reconstruction even faster. The experimental results show that our proposed gridding-based direct Fourier reconstruction is slightly more accurate than similar existing methods and presents a lower computational complexity both in terms of time and memory, thereby allowing its use on larger volumes. The algorithm is fully implemented in the open-source Xmipp package and is downloadable from http://xmipp.cnb.csic.es. Copyright © 2015 Elsevier B.V. All rights reserved.

Lipidic cubic phase injector is a viable crystal delivery system for time-resolved serial crystallography

DOE PAGES

Nogly, Przemyslaw; Panneels, Valerie; Nelson, Garrett; ...

2016-08-22

Serial femtosecond crystallography (SFX) using X-ray free-electron laser sources is an emerging method with considerable potential for time-resolved pump-probe experiments. Here we present a lipidic cubic phase SFX structure of the light-driven proton pump bacteriorhodopsin (bR) to 2.3 Å resolution and a method to investigate protein dynamics with modest sample requirement. Time-resolved SFX (TR-SFX) with a pump-probe delay of 1 ms yields difference Fourier maps compatible with the dark to M state transition of bR. Importantly, the method is very sample efficient and reduces sample consumption to about 1 mg per collected time point. Accumulation of M intermediate within themore » crystal lattice is confirmed by time-resolved visible absorption spectroscopy. Furthermore, this study provides an important step towards characterizing the complete photocycle dynamics of retinal proteins and demonstrates the feasibility of a sample efficient viscous medium jet for TR-SFX.« less

Lipidic cubic phase injector is a viable crystal delivery system for time-resolved serial crystallography

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nogly, Przemyslaw; Panneels, Valerie; Nelson, Garrett

Serial femtosecond crystallography (SFX) using X-ray free-electron laser sources is an emerging method with considerable potential for time-resolved pump-probe experiments. Here we present a lipidic cubic phase SFX structure of the light-driven proton pump bacteriorhodopsin (bR) to 2.3 Å resolution and a method to investigate protein dynamics with modest sample requirement. Time-resolved SFX (TR-SFX) with a pump-probe delay of 1 ms yields difference Fourier maps compatible with the dark to M state transition of bR. Importantly, the method is very sample efficient and reduces sample consumption to about 1 mg per collected time point. Accumulation of M intermediate within themore » crystal lattice is confirmed by time-resolved visible absorption spectroscopy. Furthermore, this study provides an important step towards characterizing the complete photocycle dynamics of retinal proteins and demonstrates the feasibility of a sample efficient viscous medium jet for TR-SFX.« less

Lipidic cubic phase injector is a viable crystal delivery system for time-resolved serial crystallography

PubMed Central

Nogly, Przemyslaw; Panneels, Valerie; Nelson, Garrett; Gati, Cornelius; Kimura, Tetsunari; Milne, Christopher; Milathianaki, Despina; Kubo, Minoru; Wu, Wenting; Conrad, Chelsie; Coe, Jesse; Bean, Richard; Zhao, Yun; Båth, Petra; Dods, Robert; Harimoorthy, Rajiv; Beyerlein, Kenneth R.; Rheinberger, Jan; James, Daniel; DePonte, Daniel; Li, Chufeng; Sala, Leonardo; Williams, Garth J.; Hunter, Mark S.; Koglin, Jason E.; Berntsen, Peter; Nango, Eriko; Iwata, So; Chapman, Henry N.; Fromme, Petra; Frank, Matthias; Abela, Rafael; Boutet, Sébastien; Barty, Anton; White, Thomas A.; Weierstall, Uwe; Spence, John; Neutze, Richard; Schertler, Gebhard; Standfuss, Jörg

2016-01-01

Serial femtosecond crystallography (SFX) using X-ray free-electron laser sources is an emerging method with considerable potential for time-resolved pump-probe experiments. Here we present a lipidic cubic phase SFX structure of the light-driven proton pump bacteriorhodopsin (bR) to 2.3 Å resolution and a method to investigate protein dynamics with modest sample requirement. Time-resolved SFX (TR-SFX) with a pump-probe delay of 1 ms yields difference Fourier maps compatible with the dark to M state transition of bR. Importantly, the method is very sample efficient and reduces sample consumption to about 1 mg per collected time point. Accumulation of M intermediate within the crystal lattice is confirmed by time-resolved visible absorption spectroscopy. This study provides an important step towards characterizing the complete photocycle dynamics of retinal proteins and demonstrates the feasibility of a sample efficient viscous medium jet for TR-SFX. PMID:27545823

Fourier transform-wavefront reconstruction for the pyramid wavefront sensor

NASA Astrophysics Data System (ADS)

Quirós-Pacheco, Fernando; Correia, Carlos; Esposito, Simone

The application of Fourier-transform reconstruction techniques to the pyramid wavefront sensor has been investigated. A preliminary study based on end-to-end simulations of an adaptive optics system with ≈40x40 subapertures and actuators shows that the performance of the Fourier-transform reconstructor (FTR) is of the same order of magnitude than the one obtained with a conventional matrix-vector multiply (MVM) method.

Polarization Ratio Determination with Two Identical Linearly Polarized Antennas

DTIC Science & Technology

2017-01-17

Fourier transform analysis of 21 measurements with one of the antennas rotating about its axis a circular polarization ratio is derived which can be...deter- mined directly from a discrete Fourier transform (DFT) of (5). However, leakage between closely spaced DFT bins requires improving the... Fourier transform and a mechanical antenna rotation to separate the principal and opposite circular polarization components followed by a basis

Scalability, Complexity and Reliability in Quantum Information Processing

DTIC Science & Technology

2007-03-01

hidden subgroup framework to abelian groups which are not finitely generated. An extension of the basic algorithm breaks the Buchmann-Williams...finding short lattice vectors . In [2], we showed that the generalization of the standard method --- random coset state preparation followed by fourier...sampling --- required exponential time for sufficiently non-abelian groups including the symmetric group , at least when the fourier transforms are

Generalized prolate spheroidal wave functions for optical finite fractional Fourier and linear canonical transforms.

PubMed

Pei, Soo-Chang; Ding, Jian-Jiun

2005-03-01

Prolate spheroidal wave functions (PSWFs) are known to be useful for analyzing the properties of the finite-extension Fourier transform (fi-FT). We extend the theory of PSWFs for the finite-extension fractional Fourier transform, the finite-extension linear canonical transform, and the finite-extension offset linear canonical transform. These finite transforms are more flexible than the fi-FT and can model much more generalized optical systems. We also illustrate how to use the generalized prolate spheroidal functions we derive to analyze the energy-preservation ratio, the self-imaging phenomenon, and the resonance phenomenon of the finite-sized one-stage or multiple-stage optical systems.

Theory and operational rules for the discrete Hankel transform.

PubMed

Baddour, Natalie; Chouinard, Ugo

2015-04-01

Previous definitions of a discrete Hankel transform (DHT) have focused on methods to approximate the continuous Hankel integral transform. In this paper, we propose and evaluate the theory of a DHT that is shown to arise from a discretization scheme based on the theory of Fourier-Bessel expansions. The proposed transform also possesses requisite orthogonality properties which lead to invertibility of the transform. The standard set of shift, modulation, multiplication, and convolution rules are derived. In addition to the theory of the actual manipulated quantities which stand in their own right, this DHT can be used to approximate the continuous forward and inverse Hankel transform in the same manner that the discrete Fourier transform is known to be able to approximate the continuous Fourier transform.

Water-induced morphology changes in BaO/γ-Al2O3 NOx storage materials: an FTIR, TPD, and time-resolved synchrotron XRD study

DOE Office of Scientific and Technical Information (OSTI.GOV)

Szanyi, Janos; Kwak, Ja Hun; Kim, Do Heui

2007-03-29

The effect of water on the morphology of BaO/Al2O3-based NOx storage materials was investigated using Fourier transform infrared spectroscopy, temperature programmed desorption, and time-resolved synchrotron X-ray diffraction techniques. The results of this multi-spectroscopy study reveal that, in the presence of water, surface Ba-nitrates convert to bulk nitrates, and water facilitates the formation of large Ba(NO3)2 particles. This process is completely reversible, i.e. after the removal of water from the storage material a significant fraction of the bulk nitrates re-convert to surface nitrates. NO2 exposure of a H2O-containing (wet) BaO/Al2O3 sample results in the formation of nitrites and bulk nitrates exclusively,more » i.e. no surface nitrates form. After further exposure to NO2, the nitrites completely convert to bulk nitrates. The amount of NOx taken up by the storage material is, however, essentially unaffected by the presence of water, regardless of whether the water was dosed prior to or after NO2 exposure. Based on the results of this study we are now able to explain most of the observations reported in the literature on the effect of water on NOx uptake on similar storage materials.« less

[Photodissociation of Acetylene and Acetone using Step-Scan Time-Resolved FTIR Emission Spectroscopy

NASA Technical Reports Server (NTRS)

McLaren, Ian A.; Wrobel, Jacek D.

1997-01-01

The photodissociation of acetylene and acetone was investigated as a function of added quenching gas pressures using step-scan time-resolved FTIR emission spectroscopy. Its main components consist of Bruker IFS88, step-scan Fourier Transform Infrared (FTIR) spectrometer coupled to a flow cell equipped with Welsh collection optics. Vibrationally excited C2H radicals were produced from the photodissociation of acetylene in the unfocused experiments. The infrared (IR) emission from these excited C2H radicals was investigated as a function of added argon pressure. Argon quenching rate constants for all C2H emission bands are of the order of 10(exp -13)cc/molecule.sec. Quenching of these radicals by acetylene is efficient, with a rate constant in the range of 10(exp -11) cc/molecule.sec. The relative intensity of the different C2H emission bands did not change with the increasing argon or acetylene pressure. However, the overall IR emission intensity decreased, for example, by more than 50% when the argon partial pressure was raised from 0.2 to 2 Torr at fixed precursor pressure of 160mTorr. These observations provide evidence for the formation of a metastable C2H2 species, which are collisionally quenched by argon or acetylene. Problems encountered in the course of the experimental work are also described.

Energetics and Dynamics of Dissociation of Deprotonated Peptides: Fragmentation of Angiotensin Analogs

DOE Office of Scientific and Technical Information (OSTI.GOV)

Laskin, Julia; Yang, Zhibo

2011-12-01

We present a first study of the energetics and dynamics of dissociation of deprotonated peptides using time- and collision-energy resolved surface-induced dissociation (SID) experiments. SID of four model peptides: RVYIHPF, HVYIHPF, DRVYIHPF, and DHVYIHPF was studied using a specially designed Fourier transform ion cyclotron resonance mass spectrometer (FT-ICR MS) configured for studying ion-surface collisions. Energy and entropy effects for the overall decomposition of the precursor ion were deduced by modeling the time- and collision energy-resolved survival curves using an RRKM based approach developed in our laboratory. The results were compared to the energetics and dynamics of dissociation of the correspondingmore » protonated species. We demonstrate that acidic peptides are less stable in the negative mode because of the low threshold associated with the kinetically hindered loss of H2O from [M-H]- ions. Comparison between the two basic peptides indicates that the lower stability of the [M-H]- ion of RVYIHPF as compared to HVYIHPF towards fragmentation is attributed to the differences in fragmentation mechanisms. Specifically, threshold energy associated with losses of NH3 and NHCNH from RVYIHPF is lower than the barrier for backbone fragmentation that dominates gas-phase decomposition of HVYIHPF. The results provide a first quantitative comparison between the energetics and dynamics of dissociation of [M+H]+ and [M-H]- ions of acidic and basic peptides.« less

Sequential measurement of conjugate variables as an alternative quantum state tomography.

PubMed

Di Lorenzo, Antonio

2013-01-04

It is shown how it is possible to reconstruct the initial state of a one-dimensional system by sequentially measuring two conjugate variables. The procedure relies on the quasicharacteristic function, the Fourier transform of the Wigner quasiprobability. The proper characteristic function obtained by Fourier transforming the experimentally accessible joint probability of observing "position" then "momentum" (or vice versa) can be expressed as a product of the quasicharacteristic function of the two detectors and that unknown of the quantum system. This allows state reconstruction through the sequence (1) data collection, (2) Fourier transform, (3) algebraic operation, and (4) inverse Fourier transform. The strength of the measurement should be intermediate for the procedure to work.

Photonic fractional Fourier transformer with a single dispersive device.

PubMed

Cuadrado-Laborde, C; Carrascosa, A; Díez, A; Cruz, J L; Andres, M V

2013-04-08

In this work we used the temporal analog of spatial Fresnel diffraction to design a temporal fractional Fourier transformer with a single dispersive device, in this way avoiding the use of quadratic phase modulators. We demonstrate that a single dispersive passive device inherently provides the fractional Fourier transform of an incident optical pulse. The relationships linking the fractional Fourier transform order and scaling factor with the dispersion parameters are derived. We first provide some numerical results in order to prove the validity of our proposal, using a fiber Bragg grating as the dispersive device. Next, we experimentally demonstrate the feasibility of this proposal by using a spool of a standard optical fiber as the dispersive device.

Time resolved infrared studies of C-H bond activation by organometallics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Asplund, M.C.

This work describes how step-scan Fourier Transform Infrared spectroscopy and visible and near infrared ultrafast lasers have been applied to the study of the photochemical activation of C-H bonds in organometallic systems, which allow for the selective breaking of C-H bonds in alkanes. The author has established the photochemical mechanism of C-H activation by Tp{sup *}Rh(CO){sub 2}(Tp{sup *} = HB-Pz{sup *}{sub 3}, Pz = 3,5-dimethylpyrazolyl) in alkane solution. The initially formed monocarbonyl forms a weak solvent complex, which undergoes a change in Tp{sup *} ligand connectivity. The final C-H bond breaking step occurs at different time scales depending on themore » structure of the alkane. In linear solvents, the time scale is <50 ns and cyclic alkanes is {approximately}200 ps. The reactivity of the Tp{sup *}Rh(CO){sub 2} system has also been studied in aromatic solvents. Here the reaction proceeds through two different pathways, with very different time scales. The first proceeds in a manner analogous to alkanes and takes <50 ns. The second proceeds through a Rh-C-C complex, and takes place on a time scale of 1.8 {micro}s.« less

Teaching Fourier optics through ray matrices

NASA Astrophysics Data System (ADS)

Moreno, I.; Sánchez-López, M. M.; Ferreira, C.; Davis, J. A.; Mateos, F.

2005-03-01

In this work we examine the use of ray-transfer matrices for teaching and for deriving some topics in a Fourier optics course, exploiting the mathematical simplicity of ray matrices compared to diffraction integrals. A simple analysis of the physical meaning of the elements of the ray matrix provides a fast derivation of the conditions to obtain the optical Fourier transform. We extend this derivation to fractional Fourier transform optical systems, and derive the order of the transform from the ray matrix. Some examples are provided to stress this point of view, both with classical and with graded index lenses. This formulation cannot replace the complete explanation of Fourier optics provided by the wave theory, but it is a complementary tool useful to simplify many aspects of Fourier optics and to relate them to geometrical optics.

Apparatus for direct-to-digital spatially-heterodyned holography

DOEpatents

Thomas, Clarence E.; Hanson, Gregory R.

2006-12-12

An apparatus operable to record a spatially low-frequency heterodyne hologram including spatially heterodyne fringes for Fourier analysis includes: a laser; a beamsplitter optically coupled to the laser; an object optically coupled to the beamsplitter; a focusing lens optically coupled to both the beamsplitter and the object; a digital recorder optically coupled to the focusing lens; and a computer that performs a Fourier transform, applies a digital filter, and performs an inverse Fourier transform. A reference beam and an object beam are focused by the focusing lens at a focal plane of the digital recorder to form a spatially low-frequency heterodyne hologram including spatially heterodyne fringes for Fourier analysis which is recorded by the digital recorder, and the computer transforms the recorded spatially low-frequency heterodyne hologram including spatially heterodyne fringes and shifts axes in Fourier space to sit on top of a heterodyne carrier frequency defined by an angle between the reference beam and the object beam and cuts off signals around an original origin before performing the inverse Fourier transform.

Time-frequency analysis of electric motors

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bentley, C.L.; Dunn, M.E.; Mattingly, J.K.

1995-12-31

Physical signals such as the current of an electric motor become nonstationary as a consequence of degraded operation and broken parts. In this instance, their power spectral densities become time dependent, and time-frequency analysis techniques become the appropriate tools for signal analysis. The first among these techniques, generally called the short-time Fourier transform (STFT) method, is the Gabor transform 2 (GT) of a signal S(t), which decomposes the signal into time-local frequency modes: where the window function, {Phi}(t-{tau}), is a normalized Gaussian. Alternatively, one can decompose the signal into its multi-resolution representation at different levels of magnification. This representation ismore » achieved by the continuous wavelet transform (CWT) where the function g(t) is a kernel of zero average belonging to a family of scaled and shifted wavelet kernels. The CWT can be interpreted as the action of a microscope that locates the signal by the shift parameter b and adjusts its magnification by changing the scale parameter a. The Fourier-transformed CWT, W,{sub g}(a, {omega}), acts as a filter that places the high-frequency content of a signal into the lower end of the scale spectrum and vice versa for the low frequencies. Signals from a motor in three different states were analyzed.« less

A class of Fourier integrals based on the electric potential of an elongated dipole.

PubMed

Skianis, Georgios Aim

2014-01-01

In the present paper the closed expressions of a class of non tabulated Fourier integrals are derived. These integrals are associated with a group of functions at space domain, which represent the electric potential of a distribution of elongated dipoles which are perpendicular to a flat surface. It is shown that the Fourier integrals are produced by the Fourier transform of the Green's function of the potential of the dipole distribution, times a definite integral in which the distribution of the polarization is involved. Therefore the form of this distribution controls the expression of the Fourier integral. Introducing various dipole distributions, the respective Fourier integrals are derived. These integrals may be useful in the quantitative interpretation of electric potential anomalies produced by elongated dipole distributions, at spatial frequency domain.

Spatially resolved XRF, XAFS, XRD, STXM and IR investigation of a natural U-rich clay

NASA Astrophysics Data System (ADS)

Denecke, M. A.; Michel, P.; Schäfer, T.; Huber, F.; Rickers, K.; Rothe, J.; Dardenne, K.; Brendebach, B.; Vitova, T.; Elie, M.

2009-11-01

Combined spatially resolved hard X-ray μ-XRF and μ-XAFS studies using an X-ray beam with micrometer dimensions at the INE-Beamline for actinide research at ANKA and Beamline L at HASYLAB with those from scanning transmission soft X-ray microscopy (STXM) and synchrotron-based Fourier transform infrared microspectroscopy (μ-FTIR) recorded with beam spots in the nanometer range are used to study a U-rich clay originating from Autunian shales in the Permian Lodève Basin (France). This argillaceous formation is a natural U deposit associated with organic matter (bitumen). Results allow us to differentiate between possible mechanisms leading to U enrichment: likely U immobilization via reaction with organic material associated with clay mineral. Such investigations support development of reliable assessment of the long term radiological safety for proposed nuclear waste disposal sites.

Resolving a Long-Standing Ambiguity: the Non-Planarity of gauche-1,3-BUTADIENE Revealed by Microwave Spectroscopy

NASA Astrophysics Data System (ADS)

Martin-Drumel, Marie-Aline; McCarthy, Michael C.; Patterson, David; Eibenberger, Sandra; Buckingham, Grant; Baraban, Joshua H.; Ellison, Barney; Stanton, John F.

2016-06-01

The preferred conformation of cis-1,3-butadiene (CH_2=CH-CH=CH_2) has been of long-standing importance in organic chemistry because of its role in Diels-Alder transition states. The molecule could adopt a planar s-cis conformation, in favor of conjugations in the carbon chain, or a non-planar gauche conformation, as a result of steric interactions between the terminal H atoms. To resolve this ambiguity, we have now measured the pure rotational spectrum of this isomer in the microwave region, unambiguously establishing a significant inertial defect, and therefore a gauche conformation. Experimental measurements of gauche-1,3-butadiene and several of its isotopologues using cavity Fourier-transform microwave (FTMW) spectroscopy in a supersonic expansion and chirped-pulse FTMW spectroscopy in a 4 K buffer gas cell will be summarized, as will new quantum chemical calculations.

Plant-based Food and Feed Protein Structure Changes Induced by Gene-transformation heating and bio-ethanol processing: A Synchrotron-based Molecular Structure and Nutrition Research Program

DOE Office of Scientific and Technical Information (OSTI.GOV)

P Yu

Unlike traditional 'wet' analytical methods which during processing for analysis often result in destruction or alteration of the intrinsic protein structures, advanced synchrotron radiation-based Fourier transform infrared microspectroscopy has been developed as a rapid and nondestructive and bioanalytical technique. This cutting-edge synchrotron-based bioanalytical technology, taking advantages of synchrotron light brightness (million times brighter than sun), is capable of exploring the molecular chemistry or structure of a biological tissue without destruction inherent structures at ultra-spatial resolutions. In this article, a novel approach is introduced to show the potential of the advanced synchrotron-based analytical technology, which can be used to study plant-basedmore » food or feed protein molecular structure in relation to nutrient utilization and availability. Recent progress was reported on using synchrotron-based bioanalytical technique synchrotron radiation-based Fourier transform infrared microspectroscopy and diffused reflectance infrared Fourier transform spectroscopy to detect the effects of gene-transformation (Application 1), autoclaving (Application 2), and bio-ethanol processing (Application 3) on plant-based food and feed protein structure changes on a molecular basis. The synchrotron-based technology provides a new approach for plant-based protein structure research at ultra-spatial resolutions at cellular and molecular levels.« less

Spectral analysis based on fast Fourier transformation (FFT) of surveillance data: the case of scarlet fever in China.

PubMed

Zhang, T; Yang, M; Xiao, X; Feng, Z; Li, C; Zhou, Z; Ren, Q; Li, X

2014-03-01

Many infectious diseases exhibit repetitive or regular behaviour over time. Time-domain approaches, such as the seasonal autoregressive integrated moving average model, are often utilized to examine the cyclical behaviour of such diseases. The limitations for time-domain approaches include over-differencing and over-fitting; furthermore, the use of these approaches is inappropriate when the assumption of linearity may not hold. In this study, we implemented a simple and efficient procedure based on the fast Fourier transformation (FFT) approach to evaluate the epidemic dynamic of scarlet fever incidence (2004-2010) in China. This method demonstrated good internal and external validities and overcame some shortcomings of time-domain approaches. The procedure also elucidated the cycling behaviour in terms of environmental factors. We concluded that, under appropriate circumstances of data structure, spectral analysis based on the FFT approach may be applicable for the study of oscillating diseases.

Intra-pulse modulation recognition using short-time ramanujan Fourier transform spectrogram

NASA Astrophysics Data System (ADS)

Ma, Xiurong; Liu, Dan; Shan, Yunlong

2017-12-01

Intra-pulse modulation recognition under negative signal-to-noise ratio (SNR) environment is a research challenge. This article presents a robust algorithm for the recognition of 5 types of radar signals with large variation range in the signal parameters in low SNR using the combination of the Short-time Ramanujan Fourier transform (ST-RFT) and pseudo-Zernike moments invariant features. The ST-RFT provides the time-frequency distribution features for 5 modulations. The pseudo-Zernike moments provide invariance properties that are able to recognize different modulation schemes on different parameter variation conditions from the ST-RFT spectrograms. Simulation results demonstrate that the proposed algorithm achieves the probability of successful recognition (PSR) of over 90% when SNR is above -5 dB with large variation range in the signal parameters: carrier frequency (CF) for all considered signals, hop size (HS) for frequency shift keying (FSK) signals, and the time-bandwidth product for Linear Frequency Modulation (LFM) signals.

A Parallel Framework with Block Matrices of a Discrete Fourier Transform for Vector-Valued Discrete-Time Signals.

PubMed

Soto-Quiros, Pablo

2015-01-01

This paper presents a parallel implementation of a kind of discrete Fourier transform (DFT): the vector-valued DFT. The vector-valued DFT is a novel tool to analyze the spectra of vector-valued discrete-time signals. This parallel implementation is developed in terms of a mathematical framework with a set of block matrix operations. These block matrix operations contribute to analysis, design, and implementation of parallel algorithms in multicore processors. In this work, an implementation and experimental investigation of the mathematical framework are performed using MATLAB with the Parallel Computing Toolbox. We found that there is advantage to use multicore processors and a parallel computing environment to minimize the high execution time. Additionally, speedup increases when the number of logical processors and length of the signal increase.

The Simulation Realization of Pavement Roughness in the Time Domain

NASA Astrophysics Data System (ADS)

XU, H. L.; He, L.; An, D.

2017-10-01

As the needs for the dynamic study on the vehicle-pavement system and the simulated vibration table test, how to simulate the pavement roughness actually is important guarantee for whether calculation and test can reflect the actual situation or not. Using the power spectral density function, the simulation of pavement roughness can be realized by Fourier inverse transform. The main idea of this method was that the spectrum amplitude and random phase were obtained separately according to the power spectrum, and then the simulation of pavement roughness was obtained in the time domain through the Fourier inverse transform (IFFT). In the process, the sampling interval (Δl) was 0.1m, and the sampling points(N) was 4096, which satisfied the accuracy requirements. Using this method, the simulate results of pavement roughness (A~H grades) were obtain in the time domain.

Billion frames per second spectrum measurement for high-repetition-rate optical pulses based on time stretching technique

NASA Astrophysics Data System (ADS)

Furukawa, Hideaki; Makino, Takeshi; Asghari, Mohammad H.; Trinh, Paul; Jalali, Bahram; Wang, Xiaomin; Kobayashi, Tetsuya; Man, Wai S.; Tsang, Kwong Shing; Wada, Naoya

2017-02-01

Single-shot and long record length spectrum measurements of high-repetition-rate optical pulses are essential for research on nonlinear dynamics as well as for applications in sensing and communication. To achieve a continuous measurements we employ the Time Stretch Dispersive Fourier Transform. We show single-shot measurements of millions of sequential pulses at high repetition rate of 1 Giga spectra per second. Results were obtained using -100 ps/nm dispersive Fourier transform module and a 50 Gsample/s real-time digitizer of 16 GHz bandwidth. Single-shot spectroscopy of 1 GHz optical pulse train was achieved with the wavelength resolution of approximately 150 pm. This instrument is ideal for observation of complex nonlinear dynamics such as switching, mode locking and soliton dynamics in high repetition rate lasers.

Gamma Knife surgery for arteriovenous malformations in the brain: integration of time-resolved contrast-enhanced magnetic resonance angiography into dosimetry planning. Technical note.

PubMed

Taschner, Christian A; Le Thuc, Vianney; Reyns, Nicolas; Gieseke, Juergen; Gauvrit, Jean-Yves; Pruvo, Jean-Pierre; Leclerc, Xavier

2007-10-01

The aim of this study was to develop an algorithm for the integration of time-resolved contrast-enhanced magnetic resonance (MR) angiography into dosimetry planning for Gamma Knife surgery (GKS) of arteriovenous malformations (AVMs) in the brain. Twelve patients harboring brain AVMs referred for GKS underwent intraarterial digital subtraction (DS) angiography and time-resolved MR angiography while wearing an externally applied cranial stereotactic frame. Time-resolved MR angiography was performed on a 1.5-tesla MR unit (Achieva, Philips Medical Systems) using contrast-enhanced 3D fast field echo sequencing with stochastic central k-space ordering. Postprocessing with interactive data language (Research Systems, Inc.) produced hybrid data sets containing dynamic angiographic information and the MR markers necessary for stereotactic transformation. Image files were sent to the Leksell GammaPlan system (Elekta) for dosimetry planning. Stereotactic transformation of the hybrid data sets containing the time-resolved MR angiography information with automatic detection of the MR markers was possible in all 12 cases. The stereotactic coordinates of vascular structures predefined from time-resolved MR angiography matched with DS angiography data in all cases. In 10 patients dosimetry planning could be performed based on time-resolved MR angiography data. In two patients, time-resolved MR angiography data alone were considered insufficient. The target volumes showed a notable shift of centers between modalities. Integration of time-resolved MR angiography data into the Leksell GammaPlan system for patients with brain AVMs is feasible. The proposed algorithm seems concise and sufficiently robust for clinical application. The quality of the time-resolved MR angiography sequencing needs further improvement.

Discrete fourier transform (DFT) analysis for applications using iterative transform methods

NASA Technical Reports Server (NTRS)

Dean, Bruce H. (Inventor)

2012-01-01

According to various embodiments, a method is provided for determining aberration data for an optical system. The method comprises collecting a data signal, and generating a pre-transformation algorithm. The data is pre-transformed by multiplying the data with the pre-transformation algorithm. A discrete Fourier transform of the pre-transformed data is performed in an iterative loop. The method further comprises back-transforming the data to generate aberration data.

Nonadiabatic laser-induced alignment of molecules: Reconstructing ⟨ θ⟩ directly from ⟨ θ2D⟩ by Fourier analysis.

PubMed

Søndergaard, Anders Aspegren; Shepperson, Benjamin; Stapelfeldt, Henrik

2017-07-07

We present an efficient, noise-robust method based on Fourier analysis for reconstructing the three-dimensional measure of the alignment degree, ⟨cos 2 θ⟩, directly from its two-dimensional counterpart, ⟨cos 2 θ 2D ⟩. The method applies to nonadiabatic alignment of linear molecules induced by a linearly polarized, nonresonant laser pulse. Our theoretical analysis shows that the Fourier transform of the time-dependent ⟨cos 2 θ 2D ⟩ trace over one molecular rotational period contains additional frequency components compared to the Fourier transform of ⟨cos 2 θ⟩. These additional frequency components can be identified and removed from the Fourier spectrum of ⟨cos 2 θ 2D ⟩. By rescaling of the remaining frequency components, the Fourier spectrum of ⟨cos 2 θ⟩ is obtained and, finally, ⟨cos 2 θ⟩ is reconstructed through inverse Fourier transformation. The method allows the reconstruction of the ⟨cos 2 θ⟩ trace from a measured ⟨cos 2 θ 2D ⟩ trace, which is the typical observable of many experiments, and thereby provides direct comparison to calculated ⟨cos 2 θ⟩ traces, which is the commonly used alignment metric in theoretical descriptions. We illustrate our method by applying it to the measurement of nonadiabatic alignment of I 2 molecules. In addition, we present an efficient algorithm for calculating the matrix elements of cos 2 θ 2D and any other observable in the symmetric top basis. These matrix elements are required in the rescaling step, and they allow for highly efficient numerical calculation of ⟨cos 2 θ 2D ⟩ and ⟨cos 2 θ⟩ in general.

STRUCTURE IN THE 3D GALAXY DISTRIBUTION: III. FOURIER TRANSFORMING THE UNIVERSE: PHASE AND POWER SPECTRA.

PubMed

Scargle, Jeffrey D; Way, M J; Gazis, P R

2017-04-10

We demonstrate the effectiveness of a relatively straightforward analysis of the complex 3D Fourier transform of galaxy coordinates derived from redshift surveys. Numerical demonstrations of this approach are carried out on a volume-limited sample of the Sloan Digital Sky Survey redshift survey. The direct unbinned transform yields a complex 3D data cube quite similar to that from the Fast Fourier Transform (FFT) of finely binned galaxy positions. In both cases deconvolution of the sampling window function yields estimates of the true transform. Simple power spectrum estimates from these transforms are roughly consistent with those using more elaborate methods. The complex Fourier transform characterizes spatial distributional properties beyond the power spectrum in a manner different from (and we argue is more easily interpreted than) the conventional multi-point hierarchy. We identify some threads of modern large scale inference methodology that will presumably yield detections in new wider and deeper surveys.

STRUCTURE IN THE 3D GALAXY DISTRIBUTION: III. FOURIER TRANSFORMING THE UNIVERSE: PHASE AND POWER SPECTRA

PubMed Central

Scargle, Jeffrey D.; Way, M. J.; Gazis, P. R.

2017-01-01

We demonstrate the effectiveness of a relatively straightforward analysis of the complex 3D Fourier transform of galaxy coordinates derived from redshift surveys. Numerical demonstrations of this approach are carried out on a volume-limited sample of the Sloan Digital Sky Survey redshift survey. The direct unbinned transform yields a complex 3D data cube quite similar to that from the Fast Fourier Transform (FFT) of finely binned galaxy positions. In both cases deconvolution of the sampling window function yields estimates of the true transform. Simple power spectrum estimates from these transforms are roughly consistent with those using more elaborate methods. The complex Fourier transform characterizes spatial distributional properties beyond the power spectrum in a manner different from (and we argue is more easily interpreted than) the conventional multi-point hierarchy. We identify some threads of modern large scale inference methodology that will presumably yield detections in new wider and deeper surveys. PMID:29628519

Structure in the 3D Galaxy Distribution: III. Fourier Transforming the Universe: Phase and Power Spectra

NASA Technical Reports Server (NTRS)

Scargle, Jeffrey D.; Way, M. J.; Gazis, P. R.

2017-01-01

We demonstrate the effectiveness of a relatively straightforward analysis of the complex 3D Fourier transform of galaxy coordinates derived from redshift surveys. Numerical demonstrations of this approach are carried out on a volume-limited sample of the Sloan Digital Sky Survey redshift survey. The direct unbinned transform yields a complex 3D data cube quite similar to that from the Fast Fourier Transform (FFT) of finely binned galaxy positions. In both cases deconvolution of the sampling window function yields estimates of the true transform. Simple power spectrum estimates from these transforms are roughly consistent with those using more elaborate methods. The complex Fourier transform characterizes spatial distributional properties beyond the power spectrum in a manner different from (and we argue is more easily interpreted than) the conventional multi-point hierarchy. We identify some threads of modern large scale inference methodology that will presumably yield detections in new wider and deeper surveys.

Response of Autonomic Nervous System to Body Positions:

NASA Astrophysics Data System (ADS)

Xu, Aiguo; Gonnella, G.; Federici, A.; Stramaglia, S.; Simone, F.; Zenzola, A.; Santostasi, R.

Two mathematical methods, the Fourier and wavelet transforms, were used to study the short term cardiovascular control system. Time series, picked from electrocardiogram and arterial blood pressure lasting 6 minutes, were analyzed in supine position (SUP), during the first (HD1) and the second parts (HD2) of 90° head down tilt, and during recovery (REC). The wavelet transform was performed using the Haar function of period T=2j (j=1,2,...,6) to obtain wavelet coefficients. Power spectra components were analyzed within three bands, VLF (0.003-0.04), LF (0.04-0.15) and HF (0.15-0.4) with the frequency unit cycle/interval. Wavelet transform demonstrated a higher discrimination among all analyzed periods than the Fourier transform. For the Fourier analysis, the LF of R-R intervals and VLF of systolic blood pressure show more evident difference for different body positions. For the wavelet analysis, the systolic blood pressures show much more evident differences than the R-R intervals. This study suggests a difference in the response of the vessels and the heart to different body positions. The partial dissociation between VLF and LF results is a physiologically relevant finding of this work.

Directional dual-tree complex wavelet packet transforms for processing quadrature signals.

PubMed

Serbes, Gorkem; Gulcur, Halil Ozcan; Aydin, Nizamettin

2016-03-01

Quadrature signals containing in-phase and quadrature-phase components are used in many signal processing applications in every field of science and engineering. Specifically, Doppler ultrasound systems used to evaluate cardiovascular disorders noninvasively also result in quadrature format signals. In order to obtain directional blood flow information, the quadrature outputs have to be preprocessed using methods such as asymmetrical and symmetrical phasing filter techniques. These resultant directional signals can be employed in order to detect asymptomatic embolic signals caused by small emboli, which are indicators of a possible future stroke, in the cerebral circulation. Various transform-based methods such as Fourier and wavelet were frequently used in processing embolic signals. However, most of the times, the Fourier and discrete wavelet transforms are not appropriate for the analysis of embolic signals due to their non-stationary time-frequency behavior. Alternatively, discrete wavelet packet transform can perform an adaptive decomposition of the time-frequency axis. In this study, directional discrete wavelet packet transforms, which have the ability to map directional information while processing quadrature signals and have less computational complexity than the existing wavelet packet-based methods, are introduced. The performances of proposed methods are examined in detail by using single-frequency, synthetic narrow-band, and embolic quadrature signals.

Automated Bayesian model development for frequency detection in biological time series.

PubMed

Granqvist, Emma; Oldroyd, Giles E D; Morris, Richard J

2011-06-24

A first step in building a mathematical model of a biological system is often the analysis of the temporal behaviour of key quantities. Mathematical relationships between the time and frequency domain, such as Fourier Transforms and wavelets, are commonly used to extract information about the underlying signal from a given time series. This one-to-one mapping from time points to frequencies inherently assumes that both domains contain the complete knowledge of the system. However, for truncated, noisy time series with background trends this unique mapping breaks down and the question reduces to an inference problem of identifying the most probable frequencies. In this paper we build on the method of Bayesian Spectrum Analysis and demonstrate its advantages over conventional methods by applying it to a number of test cases, including two types of biological time series. Firstly, oscillations of calcium in plant root cells in response to microbial symbionts are non-stationary and noisy, posing challenges to data analysis. Secondly, circadian rhythms in gene expression measured over only two cycles highlights the problem of time series with limited length. The results show that the Bayesian frequency detection approach can provide useful results in specific areas where Fourier analysis can be uninformative or misleading. We demonstrate further benefits of the Bayesian approach for time series analysis, such as direct comparison of different hypotheses, inherent estimation of noise levels and parameter precision, and a flexible framework for modelling the data without pre-processing. Modelling in systems biology often builds on the study of time-dependent phenomena. Fourier Transforms are a convenient tool for analysing the frequency domain of time series. However, there are well-known limitations of this method, such as the introduction of spurious frequencies when handling short and noisy time series, and the requirement for uniformly sampled data. Biological time series often deviate significantly from the requirements of optimality for Fourier transformation. In this paper we present an alternative approach based on Bayesian inference. We show the value of placing spectral analysis in the framework of Bayesian inference and demonstrate how model comparison can automate this procedure.

Automated Bayesian model development for frequency detection in biological time series

PubMed Central

2011-01-01

Background A first step in building a mathematical model of a biological system is often the analysis of the temporal behaviour of key quantities. Mathematical relationships between the time and frequency domain, such as Fourier Transforms and wavelets, are commonly used to extract information about the underlying signal from a given time series. This one-to-one mapping from time points to frequencies inherently assumes that both domains contain the complete knowledge of the system. However, for truncated, noisy time series with background trends this unique mapping breaks down and the question reduces to an inference problem of identifying the most probable frequencies. Results In this paper we build on the method of Bayesian Spectrum Analysis and demonstrate its advantages over conventional methods by applying it to a number of test cases, including two types of biological time series. Firstly, oscillations of calcium in plant root cells in response to microbial symbionts are non-stationary and noisy, posing challenges to data analysis. Secondly, circadian rhythms in gene expression measured over only two cycles highlights the problem of time series with limited length. The results show that the Bayesian frequency detection approach can provide useful results in specific areas where Fourier analysis can be uninformative or misleading. We demonstrate further benefits of the Bayesian approach for time series analysis, such as direct comparison of different hypotheses, inherent estimation of noise levels and parameter precision, and a flexible framework for modelling the data without pre-processing. Conclusions Modelling in systems biology often builds on the study of time-dependent phenomena. Fourier Transforms are a convenient tool for analysing the frequency domain of time series. However, there are well-known limitations of this method, such as the introduction of spurious frequencies when handling short and noisy time series, and the requirement for uniformly sampled data. Biological time series often deviate significantly from the requirements of optimality for Fourier transformation. In this paper we present an alternative approach based on Bayesian inference. We show the value of placing spectral analysis in the framework of Bayesian inference and demonstrate how model comparison can automate this procedure. PMID:21702910

Simulating first order optical systems—algorithms for and composition of discrete linear canonical transforms

NASA Astrophysics Data System (ADS)

Healy, John J.

2018-01-01

The linear canonical transforms (LCTs) are a parameterised group of linear integral transforms. The LCTs encompass a number of well-known transformations as special cases, including the Fourier transform, fractional Fourier transform, and the Fresnel integral. They relate the scalar wave fields at the input and output of systems composed of thin lenses and free space, along with other quadratic phase systems. In this paper, we perform a systematic search of all algorithms based on up to five stages of magnification, chirp multiplication and Fourier transforms. Based on that search, we propose a novel algorithm, for which we present numerical results. We compare the sampling requirements of three algorithms. Finally, we discuss some issues surrounding the composition of discrete LCTs.

Fourier transform (FT)-artifacts and power-function resolution filter in Fourier transform mass spectrometry.

PubMed

Kanawati, Basem; Bader, Theresa M; Wanczek, Karl-Peter; Li, Yan; Schmitt-Kopplin, Philippe

2017-10-15

Peak picking algorithms in mass spectrometry face the challenge of picking the correct signals from a mass spectrum. In some cases signal wiggles (side lobes) are also chosen in the produced mass list as if they were real signals. Constraints which are defined in such algorithms do not always guarantee wiggle-free accurate mass list generation out of raw mass spectra. This problem intensifies with acquisitions, which are accompanied by longer transients. Thus, the problem represents a contemporary issue, which propagates with modern high-memory digitizers and exists in both MS and MS/MS spectra. A solariX FTMS mass spectrometer with an Infinity ICR cell (Bruker Daltonics, Bremen, Germany) coupled to a 12 Tesla magnet (Magnex, UK) was used for the experimental study. Time-domain transients of several different data point lengths 512k, 1M, 2M, 4M, 8M were obtained and were Fourier-transformed to obtain frequency spectra which show the effect of the transient truncation on sinc wiggle developments in FT-ICR-MS. MATLAB simulations were also performed to investigate the origin of the Fourier transform (FT)-artifacts. A new filter has been developed to identify and remove FT-artifacts (sinc side lobes) from both frequency and mass spectra. The newly developed filter is based on distinguishing between the FWHM of the correct frequency/mass signals and the FWHM of their corresponding wiggles. The filter draws a reliable confidence limit of resolution range, within which a correct frequency/mass signal is identified. The filter is applicable over a wide mass range of metabolic interest (100-1200 amu). The origin of FT-artifacts due to time-domain transient truncations was thoroughly investigated both experimentally and by simulations in this study. A new solution for this problem with automatic recognition and elimination of these FT-artifacts (side lobes/wiggles) is provided, which is independent of any intensity thresholds, magnetic field strengths and time-domain transient lengths. Copyright © 2017 John Wiley & Sons, Ltd.

Unified commutation-pruning technique for efficient computation of composite DFTs

NASA Astrophysics Data System (ADS)

Castro-Palazuelos, David E.; Medina-Melendrez, Modesto Gpe.; Torres-Roman, Deni L.; Shkvarko, Yuriy V.

2015-12-01

An efficient computation of a composite length discrete Fourier transform (DFT), as well as a fast Fourier transform (FFT) of both time and space data sequences in uncertain (non-sparse or sparse) computational scenarios, requires specific processing algorithms. Traditional algorithms typically employ some pruning methods without any commutations, which prevents them from attaining the potential computational efficiency. In this paper, we propose an alternative unified approach with automatic commutations between three computational modalities aimed at efficient computations of the pruned DFTs adapted for variable composite lengths of the non-sparse input-output data. The first modality is an implementation of the direct computation of a composite length DFT, the second one employs the second-order recursive filtering method, and the third one performs the new pruned decomposed transform. The pruned decomposed transform algorithm performs the decimation in time or space (DIT) data acquisition domain and, then, decimation in frequency (DIF). The unified combination of these three algorithms is addressed as the DFTCOMM technique. Based on the treatment of the combinational-type hypotheses testing optimization problem of preferable allocations between all feasible commuting-pruning modalities, we have found the global optimal solution to the pruning problem that always requires a fewer or, at most, the same number of arithmetic operations than other feasible modalities. The DFTCOMM method outperforms the existing competing pruning techniques in the sense of attainable savings in the number of required arithmetic operations. It requires fewer or at most the same number of arithmetic operations for its execution than any other of the competing pruning methods reported in the literature. Finally, we provide the comparison of the DFTCOMM with the recently developed sparse fast Fourier transform (SFFT) algorithmic family. We feature that, in the sensing scenarios with sparse/non-sparse data Fourier spectrum, the DFTCOMM technique manifests robustness against such model uncertainties in the sense of insensitivity for sparsity/non-sparsity restrictions and the variability of the operating parameters.

An Investigation into the Use of Spatially-Filtered Fourier Transforms to Classify Mammary Lesions.

DTIC Science & Technology

difference in Fourier space between lesioned breast tissue which would enable accurate computer classification of benign and malignant lesions. Low...separate benign and malignant breast tissue. However, no success was achieved when using two-dimensional Fourier transform and power spectrum analysis. (Author)

Calculation of zero-offset vertical seismic profiles generated by a horizontal point force acting on the surface of an elastic half-space

USGS Publications Warehouse

Hsi-Ping, Liu

1990-01-01

Impulse responses including near-field terms have been obtained in closed form for the zero-offset vertical seismic profiles generated by a horizontal point force acting on the surface of an elastic half-space. The method is based on the correspondence principle. Through transformation of variables, the Fourier transform of the elastic impulse response is put in a form such that the Fourier transform of the corresponding anelastic impulse response can be expressed as elementary functions and their definite integrals involving distance angular frequency, phase velocities, and attenuation factors. These results are used for accurate calculation of shear-wave arrival rise times of synthetic seismograms needed for data interpretation of anelastic-attenuation measurements in near-surface sediment. -Author

Instrumental concept and preliminary performances of SIFTI: static infrared fourier transform interferometer

NASA Astrophysics Data System (ADS)

Hébert, Philippe-Jean; Cansot, E.; Pierangelo, C.; Buil, C.; Bernard, F.; Loesel, J.; Trémas, T.; Perrin, L.; Courau, E.; Casteras, C.; Maussang, I.; Simeoni, D.

2017-11-01

The SIFTI (Static Infrared Fourier Transform Interferometer) instrument aims at supporting an important part in a mission for atmospheric pollution sounding from space, by providing high spectral resolution and high Signal to Noise Ratio spectra of the atmosphere. They will allow to resolve tropospheric profiles of ozone (03) and carbon monoxide (C0), especially down to the planetary boundary layer (PBL), an altitude region of very high interest, though poorly monitored to date, for air quality and pollution monitoring. The retrieved profile of ozone, resp. C0, will contain 5 to 7, resp. 2.5 to 4, independent pieces of information. The French space agency CNES (Centre National d'Etudes Spatiales) has proposed and is studying an instrument concept for SIFTI based on a static interferometer, where the needed optical path are generated by a pair of crossed staircase fixed mirrors (replacing the moving reflector of dynamic Fourier transform interferometers like IASI or MIPAS). With the SIFTI design, a very high spectral resolution ( 0.1 cm-1 apodised) is achieved in a very compact optical setup, allowing a large throughput, hence a high SNR. The measurements are performed in the 9.5 μm band for 03 and in the 4.6 μm band for C0. The science return of the sounder can be further increased if an "intelligent pointing" process is implemented. This consists in combining the TIR sounder with a companion TIR imager, providing information on the cloud coverage in the next observed scene. 0nboard, real-time analysis of the IR image is used to command the sounder staring mirror to cloud free areas, which will maximize the probability for probing down to the surface. After the first part of the phase A, the architecture of SIFTI was studied as a trade-off between performance and resource budget. We review the main architecture and functional choices, and their advantages. The preliminary instrument concept is then presented in its main aspects and in terms of main subsystem functions. The preliminary budgets of mass, volume, size and power are also evaluated. Eventually the science performances are estimated, at instrument level and at mission level, and are compared to the specifications. To finish, the ways forward are discussed.

A Fourier collocation time domain method for numerically solving Maxwell's equations

NASA Technical Reports Server (NTRS)

Shebalin, John V.

1991-01-01

A new method for solving Maxwell's equations in the time domain for arbitrary values of permittivity, conductivity, and permeability is presented. Spatial derivatives are found by a Fourier transform method and time integration is performed using a second order, semi-implicit procedure. Electric and magnetic fields are collocated on the same grid points, rather than on interleaved points, as in the Finite Difference Time Domain (FDTD) method. Numerical results are presented for the propagation of a 2-D Transverse Electromagnetic (TEM) mode out of a parallel plate waveguide and into a dielectric and conducting medium.

Evaluation of radiation loading on finite cylindrical shells using the fast Fourier transform: A comparison with direct numerical integration.

PubMed

Liu, S X; Zou, M S

2018-03-01

The radiation loading on a vibratory finite cylindrical shell is conventionally evaluated through the direct numerical integration (DNI) method. An alternative strategy via the fast Fourier transform algorithm is put forward in this work based on the general expression of radiation impedance. To check the feasibility and efficiency of the proposed method, a comparison with DNI is presented through numerical cases. The results obtained using the present method agree well with those calculated by DNI. More importantly, the proposed calculating strategy can significantly save the time cost compared with the conventional approach of straightforward numerical integration.

Imaging open-path Fourier transform infrared spectrometer for 3D cloud profiling

NASA Astrophysics Data System (ADS)

Rentz Dupuis, Julia; Mansur, David J.; Vaillancourt, Robert; Carlson, David; Evans, Thomas; Schundler, Elizabeth; Todd, Lori; Mottus, Kathleen

2009-05-01

OPTRA is developing an imaging open-path Fourier transform infrared (I-OP-FTIR) spectrometer for 3D profiling of chemical and biological agent simulant plumes released into test ranges and chambers. An array of I-OP-FTIR instruments positioned around the perimeter of the test site, in concert with advanced spectroscopic algorithms, enables real time tomographic reconstruction of the plume. The approach is intended as a referee measurement for test ranges and chambers. This Small Business Technology Transfer (STTR) effort combines the instrumentation and spectroscopic capabilities of OPTRA, Inc. with the computed tomographic expertise of the University of North Carolina, Chapel Hill.

Interactions and Supramolecular Organization of Sulfonated Indigo and Thioindigo Dyes in Layered Hydroxide Hosts.

PubMed

Costa, Ana L; Gomes, Ana C; Pereira, Ricardo C; Pillinger, Martyn; Gonçalves, Isabel S; Pineiro, Marta; Seixas de Melo, J Sérgio

2018-01-09

Supramolecularly organized host-guest systems have been synthesized by intercalating water-soluble forms of indigo (indigo carmine, IC) and thioindigo (thioindigo-5,5'-disulfonate, TIS) in zinc-aluminum-layered double hydroxides (LDHs) and zinc-layered hydroxide salts (LHSs) by coprecipitation routes. The colors of the isolated powders were dark blue for hybrids containing only IC, purplish blue or dark lilac for cointercalated samples containing both dyes, and ruby/wine for hybrids containing only TIS. The as-synthesized and thermally treated materials were characterized by Fourier transform infrared, Fourier transform Raman, and nuclear magnetic resonance spectroscopies, powder X-ray diffraction, scanning electron microscopy, and elemental and thermogravimetric analyses. The basal spacings found for IC-LDH, TIS-LDH, IC-LHS, and TIS-LHS materials were 21.9, 21.05, 18.95, and 21.00 Å, respectively, with intermediate spacings being observed for the cointercalated samples that either decreased (LDHs) or increased (LHSs) with increasing TIS content. UV-visible and fluorescence spectroscopies (steady-state and time-resolved) were used to probe the molecular distribution of the immobilized dyes. The presence of aggregates together with the monomer units is suggested for IC-LDH, whereas for TIS-LDH, IC-LHS, and TIS-LHS, the dyes are closer to the isolated situation. Accordingly, while emission from the powder H 2 TIS is strongly quenched, an increment in the emission of about 1 order of magnitude was observed for the TIS-LDH/LHS hybrids. Double-exponential fluorescence decays were obtained and associated with two monomer species interacting differently with cointercalated water molecules. The incorporation of both TIS and IC in the LDH and LHS hosts leads to an almost complete quenching of the fluorescence, pointing to a very efficient energy transfer process from (fluorescent) TIS to (nonfluorescent) IC.

Picosecond to nanosecond reorganization of water in AOT/lecithin mixed reverse micelles of different morphology

NASA Astrophysics Data System (ADS)

Narayanan, S. Shankara; Sinha, Sudarson Sekhar; Sarkar, Rupa; Pal, Samir Kumar

2008-02-01

We report the effect of different geometrical restrictions on the dynamical properties of water using dynamic light scattering (DLS), Fourier transform infrared (FTIR) and picosecond-resolved fluorescence studies. By preparing AOT/lecithin mixed reverse micelles (RMs) of different morphologies (spherical and ellipsoidal), we have investigated the effect of the degree of confinement on the mobility of water in the mixed RMs of similar degree of hydration. The FTIR studies along with solvation dynamics of two fluorescent probes, ANS and coumarin 500 in the RMs reveal structural and dynamical information about the micellar water, which varies with the morphology of the mixed RMs.

Synchrotron FTIR Imaging For The Identification Of Cell Types Within Human Tissues

DOE Office of Scientific and Technical Information (OSTI.GOV)

Walsh, Michael J.; Pounder, F. Nell; Nasse, Michael J.

2010-02-03

The use of synchrotron Fourier Transform Infrared spectroscopy (S-FTIR) has been shown to be a very promising tool for biomedical research. S-FTIR spectroscopy allows for the fast acquisition of infrared (IR) spectra at a spatial resolution approaching the IR diffraction limit. The development of the Infrared Environmental Imaging (IRENI) beamline at the Synchrotron Radiation Center (SRC) at the University of Wisconsin-Madison has allowed for diffraction limited imaging measurements of cells in human prostate and breast tissues. This has allowed for the identification of cell types within tissues that would otherwise not have been resolvable using conventional FTIR sources.

Laser ablated hydantoin: A high resolution rotational study.

PubMed

Alonso, Elena R; Kolesniková, Lucie; Alonso, José L

2017-09-28

Laser ablation techniques coupled with broadband and narrowband Fourier transform microwave spectroscopies have allowed the high resolution rotational study of solid hydantoin, an important target in astrochemistry as a possible precursor of glycine. The complicated hyperfine structure arising from the presence of two 14 N nuclei in non-equivalent positions has been resolved and interpreted in terms of the nuclear quadrupole coupling interactions. The results reported in this work provide a solid base for the interstellar searches of hydantoin in the astrophysical surveys. The values of the nuclear quadrupole coupling constants have been also discussed in terms of the electronic environment around the respective nitrogen atom.

Development of a diffraction imaging flow cytometer

PubMed Central

Jacobs, Kenneth M.; Lu, Jun Q.

2013-01-01

Diffraction images record angle-resolved distribution of scattered light from a particle excited by coherent light and can correlate highly with the 3D morphology of a particle. We present a jet-in-fluid design of flow chamber for acquisition of clear diffraction images in a laminar flow. Diffraction images of polystyrene spheres of different diameters were acquired and found to correlate highly with the calculated ones based on the Mie theory. Fast Fourier transform analysis indicated that the measured images can be used to extract sphere diameter values. These results demonstrate the significant potentials of high-throughput diffraction imaging flow cytometry for extracting 3D morphological features of cells. PMID:19794790

Recent Advances in Laplace Transform Analytic Element Method (LT-AEM) Theory and Application to Transient Groundwater Flow

NASA Astrophysics Data System (ADS)

Kuhlman, K. L.; Neuman, S. P.

2006-12-01

Furman and Neuman (2003) proposed a Laplace Transform Analytic Element Method (LT-AEM) for transient groundwater flow. LT-AEM applies the traditionally steady-state AEM to the Laplace transformed groundwater flow equation, and back-transforms the resulting solution to the time domain using a Fourier Series numerical inverse Laplace transform method (de Hoog, et.al., 1982). We have extended the method so it can compute hydraulic head and flow velocity distributions due to any two-dimensional combination and arrangement of point, line, circular and elliptical area sinks and sources, nested circular or elliptical regions having different hydraulic properties, and areas of specified head, flux or initial condition. The strengths of all sinks and sources, and the specified head and flux values, can all vary in both space and time in an independent and arbitrary fashion. Initial conditions may vary from one area element to another. A solution is obtained by matching heads and normal fluxes along the boundary of each element. The effect which each element has on the total flow is expressed in terms of generalized Fourier series which converge rapidly (<20 terms) in most cases. As there are more matching points than unknown Fourier terms, the matching is accomplished in Laplace space using least-squares. The method is illustrated by calculating the resulting transient head and flow velocities due to an arrangement of elements in both finite and infinite domains. The 2D LT-AEM elements already developed and implemented are currently being extended to solve the 3D groundwater flow equation.

Time-frequency analysis of band-limited EEG with BMFLC and Kalman filter for BCI applications

PubMed Central

2013-01-01

Background Time-Frequency analysis of electroencephalogram (EEG) during different mental tasks received significant attention. As EEG is non-stationary, time-frequency analysis is essential to analyze brain states during different mental tasks. Further, the time-frequency information of EEG signal can be used as a feature for classification in brain-computer interface (BCI) applications. Methods To accurately model the EEG, band-limited multiple Fourier linear combiner (BMFLC), a linear combination of truncated multiple Fourier series models is employed. A state-space model for BMFLC in combination with Kalman filter/smoother is developed to obtain accurate adaptive estimation. By virtue of construction, BMFLC with Kalman filter/smoother provides accurate time-frequency decomposition of the bandlimited signal. Results The proposed method is computationally fast and is suitable for real-time BCI applications. To evaluate the proposed algorithm, a comparison with short-time Fourier transform (STFT) and continuous wavelet transform (CWT) for both synthesized and real EEG data is performed in this paper. The proposed method is applied to BCI Competition data IV for ERD detection in comparison with existing methods. Conclusions Results show that the proposed algorithm can provide optimal time-frequency resolution as compared to STFT and CWT. For ERD detection, BMFLC-KF outperforms STFT and BMFLC-KS in real-time applicability with low computational requirement. PMID:24274109

Approach for discrimination and quantification of electroactive species: kinetics difference revealed by higher harmonics of Fourier transformed sinusoidal voltammetry.

PubMed

Fang, Yishan; Huang, Xinjian; Wang, Lishi

2015-01-06

Discrimination and quantification of electroactive species are traditionally realized by a potential difference which is mainly determined by thermodynamics. However, the resolution of this approach is limited to tens of millivolts. In this paper, we described an application of Fourier transformed sinusoidal voltammetry (FT-SV) that provides a new approach for discrimination and quantitative evaluation of electroactive species, especially thermodynamic similar ones. Numerical simulation indicates that electron transfer kinetics difference between electroactive species can be revealed by the phase angle of higher order harmonics of FT-SV, and the difference can be amplified order by order. Thus, even a very subtle kinetics difference can be amplified to be distinguishable at a certain order of harmonics. This method was verified with structurally similar ferrocene derivatives which were chosen as the model systems. Although these molecules have very close redox potential (<10 mV), discrimination and selective detection were achieved by as high as the thirteenth harmonics. The results demonstrated the feasibility and reliability of the method. It was also implied that the combination of the traditional thermodynamic method and this kinetics method can form a two-dimension resolved detection method, and it has the potential to extend the resolution of voltammetric techniques to a new level.

Fourier transform profilometry (FTP) using an innovative band-pass filter for accurate 3-D surface reconstruction

NASA Astrophysics Data System (ADS)

Chen, Liang-Chia; Ho, Hsuan-Wei; Nguyen, Xuan-Loc

2010-02-01

This article presents a novel band-pass filter for Fourier transform profilometry (FTP) for accurate 3-D surface reconstruction. FTP can be employed to obtain 3-D surface profiles by one-shot images to achieve high-speed measurement. However, its measurement accuracy has been significantly influenced by the spectrum filtering process required to extract the phase information representing various surface heights. Using the commonly applied 2-D Hanning filter, the measurement errors could be up to 5-10% of the overall measuring height and it is unacceptable to various industrial application. To resolve this issue, the article proposes an elliptical band-pass filter for extracting the spectral region possessing essential phase information for reconstructing accurate 3-D surface profiles. The elliptical band-pass filter was developed and optimized to reconstruct 3-D surface models with improved measurement accuracy. Some experimental results verify that the accuracy can be effectively enhanced by using the elliptical filter. The accuracy improvement of 44.1% and 30.4% can be achieved in 3-D and sphericity measurement, respectively, when the elliptical filter replaces the traditional filter as the band-pass filtering method. Employing the developed method, the maximum measured error can be kept within 3.3% of the overall measuring range.

Structural analysis of an intact monoclonal antibody by online electrochemical reduction of disulfide bonds and Fourier transform ion cyclotron resonance mass spectrometry.

PubMed

Nicolardi, Simone; Deelder, André M; Palmblad, Magnus; van der Burgt, Yuri E M

2014-06-03

Structural confirmation and quality control of recombinant monoclonal antibodies (mAbs) by top-down mass spectrometry is still challenging due to the size of the proteins, disulfide content, and post-translational modifications such as glycosylation. In this study we have applied electrochemistry (EC) to overcome disulfide bridge complexity in top-down analysis of mAbs. To this end, an electrochemical cell was coupled directly to an electrospray ionization (ESI) source and a Fourier transform ion cyclotron resonance (FTICR) mass spectrometer (MS) equipped with a 15 T magnet. By performing online EC-assisted reduction of interchain disulfide bonds in an intact mAb, the released light chains could be selected for tandem mass spectrometry (MS/MS) analysis without interference from heavy-chain fragments. Moreover, the acquisition of full MS scans under denaturing conditions allowed profiling of all abundant mAb glycoforms. Ultrahigh-resolution FTICR-MS measurements provided fully resolved isotopic distributions of intact mAb and enabled the identification of the most abundant adducts and other interfering species. Furthermore, it was found that reduction of interchain disulfide bonds occurs in the ESI source dependent on capillary voltage and solvent composition. This phenomenon was systematically evaluated and compared with the results obtained from reduction in the electrochemical cell.

Estimation of multiple accelerated motions using chirp-Fourier transform and clustering.

PubMed

Alexiadis, Dimitrios S; Sergiadis, George D

2007-01-01

Motion estimation in the spatiotemporal domain has been extensively studied and many methodologies have been proposed, which, however, cannot handle both time-varying and multiple motions. Extending previously published ideas, we present an efficient method for estimating multiple, linearly time-varying motions. It is shown that the estimation of accelerated motions is equivalent to the parameter estimation of superpositioned chirp signals. From this viewpoint, one can exploit established signal processing tools such as the chirp-Fourier transform. It is shown that accelerated motion results in energy concentration along planes in the 4-D space: spatial frequencies-temporal frequency-chirp rate. Using fuzzy c-planes clustering, we estimate the plane/motion parameters. The effectiveness of our method is verified on both synthetic as well as real sequences and its advantages are highlighted.

Application of pulsed-gradient Fourier transform nuclear magnetic resonance to the study of self-diffusion of phospholipid vesicles.

PubMed

McDonald, G G; Vanderkooi, J M

1975-05-20

A pulsed-gradient Fourier transform nuclear magnetic resonance (NMR) technique was appplied to the study of diffusion of phospholipid vesicles. The diffusion coefficient of dimyristoyllecithin vesicles (DML) in a D2O-phospahte buffer at 37 degrees is D = 1.9 TIMES 10(-6) cm2/sec. In a solution made viscous by DNA addition, the diffusion coefficient of DML vesicles was 3.5 times 10(-7) cm2/sec. These values compare favorably with the diffusion rate for liposomes as determined by ultracentrifugation and by Stokes law calculation. The data suggest that DML diffusion is controlled primarily by whole liposome migration as opposed to movement of individual molecules within the liposome, liposome rotation, or fast exchange between lecithin molecules in solution and in vesicles.

Time efficient Gabor fused master slave optical coherence tomography

NASA Astrophysics Data System (ADS)

Cernat, Ramona; Bradu, Adrian; Rivet, Sylvain; Podoleanu, Adrian

2018-02-01

In this paper the benefits in terms of operation time that Master/Slave (MS) implementation of optical coherence tomography can bring in comparison to Gabor fused (GF) employing conventional fast Fourier transform based OCT are presented. The Gabor Fusion/Master Slave Optical Coherence Tomography architecture proposed here does not need any data stitching. Instead, a subset of en-face images is produced for each focus position inside the sample to be imaged, using a reduced number of theoretically inferred Master masks. These en-face images are then assembled into a final volume. When the channelled spectra are digitized into 1024 sampling points, and more than 4 focus positions are required to produce the final volume, the Master Slave implementation of the instrument is faster than the conventional fast Fourier transform based procedure.

A Primer of Fourier Transform NMR.

ERIC Educational Resources Information Center

Macomber, Roger S.

1985-01-01

Fourier transform nuclear magnetic resonance (NMR) is a new spectroscopic technique that is often omitted from undergraduate curricula because of lack of instructional materials. Therefore, information is provided to introduce students to the technique of data collection and transformation into the frequency domain. (JN)

Geometric Representations for Discrete Fourier Transforms

NASA Technical Reports Server (NTRS)

Cambell, C. W.

1986-01-01

Simple geometric representations show symmetry and periodicity of discrete Fourier transforms (DFT's). Help in visualizing requirements for storing and manipulating transform value in computations. Representations useful in any number of dimensions, but particularly in one-, two-, and three-dimensional cases often encountered in practice.

Sparsity guided empirical wavelet transform for fault diagnosis of rolling element bearings

NASA Astrophysics Data System (ADS)

Wang, Dong; Zhao, Yang; Yi, Cai; Tsui, Kwok-Leung; Lin, Jianhui

2018-02-01

Rolling element bearings are widely used in various industrial machines, such as electric motors, generators, pumps, gearboxes, railway axles, turbines, and helicopter transmissions. Fault diagnosis of rolling element bearings is beneficial to preventing any unexpected accident and reducing economic loss. In the past years, many bearing fault detection methods have been developed. Recently, a new adaptive signal processing method called empirical wavelet transform attracts much attention from readers and engineers and its applications to bearing fault diagnosis have been reported. The main problem of empirical wavelet transform is that Fourier segments required in empirical wavelet transform are strongly dependent on the local maxima of the amplitudes of the Fourier spectrum of a signal, which connotes that Fourier segments are not always reliable and effective if the Fourier spectrum of the signal is complicated and overwhelmed by heavy noises and other strong vibration components. In this paper, sparsity guided empirical wavelet transform is proposed to automatically establish Fourier segments required in empirical wavelet transform for fault diagnosis of rolling element bearings. Industrial bearing fault signals caused by single and multiple railway axle bearing defects are used to verify the effectiveness of the proposed sparsity guided empirical wavelet transform. Results show that the proposed method can automatically discover Fourier segments required in empirical wavelet transform and reveal single and multiple railway axle bearing defects. Besides, some comparisons with three popular signal processing methods including ensemble empirical mode decomposition, the fast kurtogram and the fast spectral correlation are conducted to highlight the superiority of the proposed method.

40 CFR 98.414 - Monitoring and QA/QC requirements.

Code of Federal Regulations, 2011 CFR

2011-07-01

... appropriate detector, infrared (IR), fourier transform infrared (FTIR), and nuclear magnetic resonance (NMR... Compounds by Extractive Direct Interface Fourier Transform Infrared (FTIR) Spectroscopy (incorporated by...

40 CFR 98.414 - Monitoring and QA/QC requirements.

Code of Federal Regulations, 2012 CFR

2012-07-01

... appropriate detector, infrared (IR), fourier transform infrared (FTIR), and nuclear magnetic resonance (NMR... Compounds by Extractive Direct Interface Fourier Transform Infrared (FTIR) Spectroscopy (incorporated by...

40 CFR 98.414 - Monitoring and QA/QC requirements.

Code of Federal Regulations, 2014 CFR

2014-07-01

... appropriate detector, infrared (IR), fourier transform infrared (FTIR), and nuclear magnetic resonance (NMR... Compounds by Extractive Direct Interface Fourier Transform Infrared (FTIR) Spectroscopy (incorporated by...

40 CFR 98.414 - Monitoring and QA/QC requirements.

Code of Federal Regulations, 2013 CFR

2013-07-01

... appropriate detector, infrared (IR), fourier transform infrared (FTIR), and nuclear magnetic resonance (NMR... Compounds by Extractive Direct Interface Fourier Transform Infrared (FTIR) Spectroscopy (incorporated by...

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hudgins, L.H.

After a brief review of the elementary properties of Fourier Transforms, the Wavelet Transform is defined in Part I. Basic results are given for admissable wavelets. The Multiresolution Analysis, or MRA (a mathematical structure which unifies a large class of wavelets with Quadrature Mirror Filters) is then introduced. Some fundamental aspects of wavelet design are then explored. The Discrete Wavelet Transform is discussed and, in the context of an MRA, is seen to supply a Fast Wavelet Transform which competes with the Fast Fourier Transform for efficiency. In Part II, the Wavelet Transform is developed in terms of the scalemore » number variable s instead of the scale length variable a where a = 1/s. Basic results such as the admissibility condition, conservation of energy, and the reconstruction theorem are proven in this context. After reviewing some motivation for the usual Fourier power spectrum, a definition is given for the wavelet power spectrum. This `spectral density` is then intepreted in the context of spectral estimation theory. Parseval`s theorem for Wavelets then leads naturally to the Wavelet Cross Spectrum, Wavelet Cospectrum, and Wavelet Quadrature Spectrum. Wavelet Transforms are then applied in Part III to the analysis of atmospheric turbulence. Data collected over the ocean is examined in the wavelet transform domain for underlying structure. A brief overview of atmospheric turbulence is provided. Then the overall method of applying Wavelet Transform techniques to time series data is described. A trace study is included, showing some of the aspects of choosing the computational algorithm, and selection of a specific analyzing wavelet. A model for generating synthetic turbulence data is developed, and seen to yield useful results in comparing with real data for structural transitions. Results from the theory of Wavelet Spectral Estimation and Wavelength Cross-Transforms are applied to studying the momentum transport and the heat flux.« less

Numerical study of the stress state of a deformation twin in magnesium

DOE PAGES

Arul Kumar, M.; Kanjarla, A. K.; Niezgoda, S. R.; ...

2014-11-26

Here, we present a numerical study of the distribution of the local stress state associated with deformation twinning in Mg, both inside the twinned domain and in its immediate neighborhood, due to the accommodation of the twinning transformation shear. A full-field elastoviscoplastic formulation based on fast Fourier transformation is modified to include the shear transformation strain associated with deformation twinning. We performed two types of twinning transformation simulations with: (i) the twin completely embedded inside a single crystal and (ii) the twin front terminating at a grain boundary. We show that: (a) the resulting stress distribution is more strongly determinedmore » by the shear transformation than by the intragranular character of the twin or the orientation of the neighboring grain; (b) the resolved shear stress on the twin plane along the twin direction is inhomogeneous along the twin–parent interface; and (c) there are substantial differences in the average values of the shear stress in the twin and in the parent grain that contains the twin. We discuss the effect of these local stresses on twin propagation and growth, and the implications of our findings for the modeling of deformation twinning.« less

Numerical study of the stress state of a deformation twin in magnesium

DOE Office of Scientific and Technical Information (OSTI.GOV)

Arul Kumar, M.; Kanjarla, A. K.; Niezgoda, S. R.

2015-02-01

We present here a numerical study of the distribution of the local stress state associated with deformation twinning in Mg, both inside the twinned domain and in its immediate neighborhood, due to the accommodation of the twinning transformation shear. A full-field elastoviscoplastic formulation based on fast Fourier transformation is modified to include the shear transformation strain associated with deformation twinning. We have performed two types of twinning transformation simulations with: (i) the twin completely embedded inside a single crystal and (ii) the twin front terminating at a grain boundary. We show that: (a) the resulting stress distribution is more stronglymore » determined by the shear transformation than by the intragranular character of the twin or the orientation of the neighboring grain; (b) the resolved shear stress on the twin plane along the twin direction is inhomogeneous along the twin–parent interface; and (c) there are substantial differences in the average values of the shear stress in the twin and in the parent grain that contains the twin. We discuss the effect of these local stresses on twin propagation and growth, and the implications of our findings for the modeling of deformation twinning.« less

Fast IR laser mapping ellipsometry for the study of functional organic thin films.

PubMed

Furchner, Andreas; Sun, Guoguang; Ketelsen, Helge; Rappich, Jörg; Hinrichs, Karsten

2015-03-21

Fast infrared mapping with sub-millimeter lateral resolution as well as time-resolved infrared studies of kinetic processes of functional organic thin films require a new generation of infrared ellipsometers. We present a novel laboratory-based infrared (IR) laser mapping ellipsometer, in which a laser is coupled to a variable-angle rotating analyzer ellipsometer. Compared to conventional Fourier-transform infrared (FT-IR) ellipsometers, the IR laser ellipsometer provides ten- to hundredfold shorter measurement times down to 80 ms per measured spot, as well as about tenfold increased lateral resolution of 120 μm, thus enabling mapping of small sample areas with thin-film sensitivity. The ellipsometer, equipped with a HeNe laser emitting at about 2949 cm(-1), was applied for the optical characterization of inhomogeneous poly(3-hexylthiophene) [P3HT] and poly(N-isopropylacrylamide) [PNIPAAm] organic thin films used for opto-electronics and bioapplications. With the constant development of tunable IR laser sources, laser-based infrared ellipsometry is a promising technique for fast in-depth mapping characterization of thin films and blends.

Analysis and application of Fourier transform spectroscopy in atmospheric remote sensing

NASA Technical Reports Server (NTRS)

Park, J. H.

1984-01-01

An analysis method for Fourier transform spectroscopy is summarized with applications to various types of distortion in atmospheric absorption spectra. This analysis method includes the fast Fourier transform method for simulating the interferometric spectrum and the nonlinear least-squares method for retrieving the information from a measured spectrum. It is shown that spectral distortions can be simulated quite well and that the correct information can be retrieved from a distorted spectrum by this analysis technique.

Implementation of the semiclassical quantum Fourier transform in a scalable system.

PubMed

Chiaverini, J; Britton, J; Leibfried, D; Knill, E; Barrett, M D; Blakestad, R B; Itano, W M; Jost, J D; Langer, C; Ozeri, R; Schaetz, T; Wineland, D J

2005-05-13

We report the implementation of the semiclassical quantum Fourier transform in a system of three beryllium ion qubits (two-level quantum systems) confined in a segmented multizone trap. The quantum Fourier transform is the crucial final step in Shor's algorithm, and it acts on a register of qubits to determine the periodicity of the quantum state's amplitudes. Because only probability amplitudes are required for this task, a more efficient semiclassical version can be used, for which only single-qubit operations conditioned on measurement outcomes are required. We apply the transform to several input states of different periodicities; the results enable the location of peaks corresponding to the original periods. This demonstration incorporates the key elements of a scalable ion-trap architecture, suggesting the future capability of applying the quantum Fourier transform to a large number of qubits as required for a useful quantum factoring algorithm.

Fourier-domain angle-resolved low coherence interferometry for clinical detection of dysplasia

NASA Astrophysics Data System (ADS)

Terry, Neil G.; Zhu, Yizheng; Wax, Adam

2010-02-01

Improved methods for detecting dysplasia, or pre-cancerous growth are a current clinical need, particularly in the esophagus. The currently accepted method of random biopsy and histological analysis provides only a limited examination of tissue in question while being coupled with a long time delay for diagnosis. Light scattering spectroscopy, in contrast, allows for inspection of the cellular structure and organization of tissue in vivo. Fourier-domain angle-resolved low-coherence interferometry (a/LCI) is a novel light scattering spectroscopy technique that provides quantitative depth-resolved morphological measurements of the size and optical density of the examined cell nuclei, which are characteristic biomarkers of dysplasia. Previously, clinical viability of the a/LCI system was demonstrated through analysis of ex vivo human esophageal tissue in Barrett's esophagus patients using a portable a/LCI, as was the development of a clinical a/LCI system. Data indicating the feasibility of the technique in other organ sites (colon, oral cavity) will be presented. We present an adaptation of the a/LCI system that will be used to investigate the presence of dysplasia in vivo in Barrett's esophagus patients.

The discrete Fourier transform algorithm for determining decay constants—Implementation using a field programmable gate array

NASA Astrophysics Data System (ADS)

Bostrom, G.; Atkinson, D.; Rice, A.

2015-04-01

Cavity ringdown spectroscopy (CRDS) uses the exponential decay constant of light exiting a high-finesse resonance cavity to determine analyte concentration, typically via absorption. We present a high-throughput data acquisition system that determines the decay constant in near real time using the discrete Fourier transform algorithm on a field programmable gate array (FPGA). A commercially available, high-speed, high-resolution, analog-to-digital converter evaluation board system is used as the platform for the system, after minor hardware and software modifications. The system outputs decay constants at maximum rate of 4.4 kHz using an 8192-point fast Fourier transform by processing the intensity decay signal between ringdown events. We present the details of the system, including the modifications required to adapt the evaluation board to accurately process the exponential waveform. We also demonstrate the performance of the system, both stand-alone and incorporated into our existing CRDS system. Details of FPGA, microcontroller, and circuitry modifications are provided in the Appendix and computer code is available upon request from the authors.

[Using 2-DCOS to identify the molecular spectrum peaks for the isomer in the multi-component mixture gases Fourier transform infrared analysis].

PubMed

Zhao, An-Xin; Tang, Xiao-Jun; Zhang, Zhong-Hua; Liu, Jun-Hua

2014-10-01

The generalized two-dimensional correlation spectroscopy and Fourier transform infrared were used to identify hydrocarbon isomers in the mixed gases for absorption spectra resolution enhancement. The Fourier transform infrared spectrum of n-butane and iso-butane and the two-dimensional correlation infrared spectrum of concentration perturbation were used for analysis as an example. The all band and the main absorption peak wavelengths of Fourier transform infrared spectrum for single component gas showed that the spectra are similar, and if they were mixed together, absorption peaks overlap and peak is difficult to identify. The synchronous and asynchronous spectrum of two-dimensional correlation spectrum can clearly identify the iso-butane and normal butane and their respective characteristic absorption peak intensity. Iso-butane has strong absorption characteristics spectrum lines at 2,893, 2,954 and 2,893 cm(-1), and n-butane at 2,895 and 2,965 cm(-1). The analysis result in this paper preliminary verified that the two-dimensional infrared correlation spectroscopy can be used for resolution enhancement in Fourier transform infrared spectrum quantitative analysis.

[Detection of Heart Rate of Fetal ECG Based on STFT and BSS].

PubMed

Wang, Xu; Cai, Kun

2016-01-01

Changes in heart rate of fetal is function regulating performance of the circulatory system and the central nervous system, it is significant to detect heart rate of fetus in perinatal fetal. This paper puts forward the fetal heart rate detection method based on short time Fourier transform and blind source separation. First of all, the mixed ECG signal was preprocessed, and then the wavelet transform technique was used to separate the fetal ECG signal with noise from mixed ECG signal, after that, the short-time Fourier transform and the blind separation were carried on it, and then calculated the correlation coefficient of it, Finally, An independent component that it has strongest correlation with the original signal was selected to make FECG peak detection and calculated the fetal instantaneous heart rate. The experimental results show that the method can improve the detection rate of the FECG peak (R), and it has high accuracy in fixing peak(R) location in the case of low signal-noise ratio.

Supercontinuum Fourier transform spectrometry with balanced detection on a single photodiode

DOE Office of Scientific and Technical Information (OSTI.GOV)

Goncharov, Vasily V.; Hall, Gregory E., E-mail: gehall@bnl.gov

We demonstrate a method of combining a supercontinuum light source with a commercial Fourier transform spectrometer, using a novel approach to dual-beam balanced detection, implemented with phase-sensitive detection on a single light detector. A 40 dB reduction in the relative intensity noise is achieved for broadband light, analogous to conventional balanced detection methods using two matched photodetectors. Unlike conventional balanced detection, however, this method exploits the time structure of the broadband source to interleave signal and reference pulse trains in the time domain, recording the broadband differential signal at the fundamental pulse repetition frequency of the supercontinuum. The method ismore » capable of real-time correction for instability in the supercontinuum spectral structure over a broad range of wavelengths and is compatible with commercially designed spectrometers. A proof-of-principle experimental setup is demonstrated for weak absorption in the 1500-1600 nm region.« less

[Combustion temperature measurement of pyrotechnic composition using remote sensing Fourier transform infrared spectrometry].

PubMed

Zhou, Xin-li; Li, Yan; Liu, Zu-liang; Zhu, Chang-jiang; Wang, Jun-de; Lu, Chun-xu

2002-10-01

In this paper, combustion characterization of pyrotechnic composition is investigated using a remote sensing Fourier transform infrared spectrometry. The emission spectra have been recorded between 4,700 and 740 cm-1 with a spectral resolution of 4 cm-1. The combustion temperature can be determined remotely from spectral line intensity distribution of the fine structure of the emission fundamental band of gaseous products such as HF. The relationship between combustion temperature and combustion time has been given. Results show that there is a violent mutative temperature field with bigger temperature gradient near combustion surface. It reveals that the method of temperature measurement using remote sensing FTIR for flame temperature of unstable, violent and short time combustion on real time is a rapid, accurate and sensitive technique without interference the flame temperature field. Potential prospects of temperature measurement, gas product concentration measurement and combustion mechanism are also revealed.

Multifractal surrogate-data generation algorithm that preserves pointwise Hölder regularity structure, with initial applications to turbulence

NASA Astrophysics Data System (ADS)

Keylock, C. J.

2017-03-01

An algorithm is described that can generate random variants of a time series while preserving the probability distribution of original values and the pointwise Hölder regularity. Thus, it preserves the multifractal properties of the data. Our algorithm is similar in principle to well-known algorithms based on the preservation of the Fourier amplitude spectrum and original values of a time series. However, it is underpinned by a dual-tree complex wavelet transform rather than a Fourier transform. Our method, which we term the iterated amplitude adjusted wavelet transform can be used to generate bootstrapped versions of multifractal data, and because it preserves the pointwise Hölder regularity but not the local Hölder regularity, it can be used to test hypotheses concerning the presence of oscillating singularities in a time series, an important feature of turbulence and econophysics data. Because the locations of the data values are randomized with respect to the multifractal structure, hypotheses about their mutual coupling can be tested, which is important for the velocity-intermittency structure of turbulence and self-regulating processes.

Pursuing optimal electric machines transient diagnosis: The adaptive slope transform

NASA Astrophysics Data System (ADS)

Pons-Llinares, Joan; Riera-Guasp, Martín; Antonino-Daviu, Jose A.; Habetler, Thomas G.

2016-12-01

The aim of this paper is to introduce a new linear time-frequency transform to improve the detection of fault components in electric machines transient currents. Linear transforms are analysed from the perspective of the atoms used. A criterion to select the atoms at every point of the time-frequency plane is proposed, taking into account the characteristics of the searched component at each point. This criterion leads to the definition of the Adaptive Slope Transform, which enables a complete and optimal capture of the different components evolutions in a transient current. A comparison with conventional linear transforms (Short-Time Fourier Transform and Wavelet Transform) is carried out, showing their inherent limitations. The approach is tested with laboratory and field motors, and the Lower Sideband Harmonic is captured for the first time during an induction motor startup and subsequent load oscillations, accurately tracking its evolution.

A BASIC program for the removal of noise from reaction traces using Fourier filtering.

PubMed

Brittain, T

1989-04-01

Software for the removal of noise from reaction curves using the principle of Fourier filtering has been written in BASIC to execute on a PC. The program inputs reaction traces which are subjected to a rotation-inversion process, to produce functions suitable for Fourier analysis. Fourier transformation into the frequency domain is followed by multiplication of the transform by a rectangular filter function, to remove the noise frequencies. Inverse transformation then yields a noise-reduced reaction trace suitable for further analysis. The program is interactive at each stage and could easily be modified to remove noise from a range of input data types.

Method for determining and displaying the spacial distribution of a spectral pattern of received light

DOEpatents

Bennett, C.L.

1996-07-23

An imaging Fourier transform spectrometer is described having a Fourier transform infrared spectrometer providing a series of images to a focal plane array camera. The focal plane array camera is clocked to a multiple of zero crossing occurrences as caused by a moving mirror of the Fourier transform infrared spectrometer and as detected by a laser detector such that the frame capture rate of the focal plane array camera corresponds to a multiple of the zero crossing rate of the Fourier transform infrared spectrometer. The images are transmitted to a computer for processing such that representations of the images as viewed in the light of an arbitrary spectral ``fingerprint`` pattern can be displayed on a monitor or otherwise stored and manipulated by the computer. 2 figs.

THE PSTD ALGORITHM: A TIME-DOMAIN METHOD REQUIRING ONLY TWO CELLS PER WAVELENGTH. (R825225)

EPA Science Inventory

A pseudospectral time-domain (PSTD) method is developed for solutions of Maxwell's equations. It uses the fast Fourier transform (FFT), instead of finite differences on conventional finite-difference-time-domain (FDTD) methods, to represent spatial derivatives. Because the Fourie...

Fourier Collocation Approach With Mesh Refinement Method for Simulating Transit-Time Ultrasonic Flowmeters Under Multiphase Flow Conditions.

PubMed

Simurda, Matej; Duggen, Lars; Basse, Nils T; Lassen, Benny

2018-02-01

A numerical model for transit-time ultrasonic flowmeters operating under multiphase flow conditions previously presented by us is extended by mesh refinement and grid point redistribution. The method solves modified first-order stress-velocity equations of elastodynamics with additional terms to account for the effect of the background flow. Spatial derivatives are calculated by a Fourier collocation scheme allowing the use of the fast Fourier transform, while the time integration is realized by the explicit third-order Runge-Kutta finite-difference scheme. The method is compared against analytical solutions and experimental measurements to verify the benefit of using mapped grids. Additionally, a study of clamp-on and in-line ultrasonic flowmeters operating under multiphase flow conditions is carried out.

Efficient detection of a CW signal with a linear frequency drift

NASA Technical Reports Server (NTRS)

Swarztrauber, Paul N.; Bailey, David H.

1989-01-01

An efficient method is presented for the detection of a continuous wave (CW) signal with a frequency drift that is linear in time. Signals of this type occur in transmissions between any two locations that are accelerating relative to one another, e.g., transmissions from the Voyager spacecraft. We assume that both the frequency and the drift are unknown. We also assume that the signal is weak compared to the Gaussian noise. The signal is partitioned into subsequences whose discrete Fourier transforms provide a sequence of instantaneous spectra at equal time intervals. These spectra are then accumulated with a shift that is proportional to time. When the shift is equal to the frequency drift, the signal to noise ratio increases and detection occurs. Here, we show how to compute these accumulations for many shifts in an efficient manner using a variety of Fast Fourier Transformations (FFT). Computing time is proportional to L log L where L is the length of the time series.

Advance in ERG Analysis: From Peak Time and Amplitude to Frequency, Power, and Energy

PubMed Central

Lina, Jean-Marc; Lachapelle, Pierre

2014-01-01

Purpose. To compare time domain (TD: peak time and amplitude) analysis of the human photopic electroretinogram (ERG) with measures obtained in the frequency domain (Fourier analysis: FA) and in the time-frequency domain (continuous (CWT) and discrete (DWT) wavelet transforms). Methods. Normal ERGs (n = 40) were analyzed using traditional peak time and amplitude measurements of the a- and b-waves in the TD and descriptors extracted from FA, CWT, and DWT. Selected descriptors were also compared in their ability to monitor the long-term consequences of disease process. Results. Each method extracted relevant information but had distinct limitations (i.e., temporal and frequency resolutions). The DWT offered the best compromise by allowing us to extract more relevant descriptors of the ERG signal at the cost of lesser temporal and frequency resolutions. Follow-ups of disease progression were more prolonged with the DWT (max 29 years compared to 13 with TD). Conclusions. Standardized time domain analysis of retinal function should be complemented with advanced DWT descriptors of the ERG. This method should allow more sensitive/specific quantifications of ERG responses, facilitate follow-up of disease progression, and identify diagnostically significant changes of ERG waveforms that are not resolved when the analysis is only limited to time domain measurements. PMID:25061605

Time-dependent Electron Acceleration in Blazar Transients: X-Ray Time Lags and Spectral Formation

NASA Astrophysics Data System (ADS)

Lewis, Tiffany R.; Becker, Peter A.; Finke, Justin D.

2016-06-01

Electromagnetic radiation from blazar jets often displays strong variability, extending from radio to γ-ray frequencies. In a few cases, this variability has been characterized using Fourier time lags, such as those detected in the X-rays from Mrk 421 using BeppoSAX. The lack of a theoretical framework to interpret the data has motivated us to develop a new model for the formation of the X-ray spectrum and the time lags in blazar jets based on a transport equation including terms describing stochastic Fermi acceleration, synchrotron losses, shock acceleration, adiabatic expansion, and spatial diffusion. We derive the exact solution for the Fourier transform of the electron distribution and use it to compute the Fourier transform of the synchrotron radiation spectrum and the associated X-ray time lags. The same theoretical framework is also used to compute the peak flare X-ray spectrum, assuming that a steady-state electron distribution is achieved during the peak of the flare. The model parameters are constrained by comparing the theoretical predictions with the observational data for Mrk 421. The resulting integrated model yields, for the first time, a complete first-principles physical explanation for both the formation of the observed time lags and the shape of the peak flare X-ray spectrum. It also yields direct estimates of the strength of the shock and the stochastic magnetohydrodynamical wave acceleration components in the Mrk 421 jet.

An interior penalty stabilised incompressible discontinuous Galerkin-Fourier solver for implicit large eddy simulations

NASA Astrophysics Data System (ADS)

Ferrer, Esteban

2017-11-01

We present an implicit Large Eddy Simulation (iLES) h / p high order (≥2) unstructured Discontinuous Galerkin-Fourier solver with sliding meshes. The solver extends the laminar version of Ferrer and Willden, 2012 [34], to enable the simulation of turbulent flows at moderately high Reynolds numbers in the incompressible regime. This solver allows accurate flow solutions of the laminar and turbulent 3D incompressible Navier-Stokes equations on moving and static regions coupled through a high order sliding interface. The spatial discretisation is provided by the Symmetric Interior Penalty Discontinuous Galerkin (IP-DG) method in the x-y plane coupled with a purely spectral method that uses Fourier series and allows efficient computation of spanwise periodic three-dimensional flows. Since high order methods (e.g. discontinuous Galerkin and Fourier) are unable to provide enough numerical dissipation to enable under-resolved high Reynolds computations (i.e. as necessary in the iLES approach), we adapt the laminar version of the solver to increase (controllably) the dissipation and enhance the stability in under-resolved simulations. The novel stabilisation relies on increasing the penalty parameter included in the DG interior penalty (IP) formulation. The latter penalty term is included when discretising the linear viscous terms in the incompressible Navier-Stokes equations. These viscous penalty fluxes substitute the stabilising effect of non-linear fluxes, which has been the main trend in implicit LES discontinuous Galerkin approaches. The IP-DG penalty term provides energy dissipation, which is controlled by the numerical jumps at element interfaces (e.g. large in under-resolved regions) such as to stabilise under-resolved high Reynolds number flows. This dissipative term has minimal impact in well resolved regions and its implicit treatment does not restrict the use of large time steps, thus providing an efficient stabilization mechanism for iLES. The IP-DG stabilisation is complemented with a Spectral Vanishing Viscosity (SVV) method, in the z-direction, to enhance stability in the continuous Fourier space. The coupling between the numerical viscosity in the DG plane and the SVV damping, provides an efficient approach to stabilise high order methods at moderately high Reynolds numbers. We validate the formulation for three turbulent flow cases: a circular cylinder at Re = 3900, a static and pitch oscillating NACA 0012 airfoil at Re = 10000 and finally a rotating vertical-axis turbine at Re = 40000, with Reynolds based on the circular diameter, airfoil chord and turbine diameter, respectively. All our results compare favourably with published direct numerical simulations, large eddy simulations or experimental data. We conclude that the DG-Fourier high order solver, with IP-SVV stabilisation, proves to be a valuable tool to predict turbulent flows and associated statistics for both static and rotating machinery.

Nonlinear Fourier transform—towards the construction of nonlinear Fourier modes

NASA Astrophysics Data System (ADS)

Saksida, Pavle

2018-01-01

We study a version of the nonlinear Fourier transform associated with ZS-AKNS systems. This version is suitable for the construction of nonlinear analogues of Fourier modes, and for the perturbation-theoretic study of their superposition. We provide an iterative scheme for computing the inverse of our transform. The relevant formulae are expressed in terms of Bell polynomials and functions related to them. In order to prove the validity of our iterative scheme, we show that our transform has the necessary analytic properties. We show that up to order three of the perturbation parameter, the nonlinear Fourier mode is a complex sinusoid modulated by the second Bernoulli polynomial. We describe an application of the nonlinear superposition of two modes to a problem of transmission through a nonlinear medium.

40 CFR 98.224 - Monitoring and QA/QC requirements.

Code of Federal Regulations, 2014 CFR

2014-07-01

... Inorganic Emissions by Extractive Fourier Transform Infrared (FTIR) Spectroscopy. (2) ASTM D6348-03 Standard Test Method for Determination of Gaseous Compounds by Extractive Direct Interface Fourier Transform...

40 CFR 98.224 - Monitoring and QA/QC requirements.

Code of Federal Regulations, 2012 CFR

2012-07-01

... Inorganic Emissions by Extractive Fourier Transform Infrared (FTIR) Spectroscopy. (2) ASTM D6348-03 Standard Test Method for Determination of Gaseous Compounds by Extractive Direct Interface Fourier Transform...

40 CFR 98.224 - Monitoring and QA/QC requirements.

Code of Federal Regulations, 2011 CFR

2011-07-01

... Inorganic Emissions by Extractive Fourier Transform Infrared (FTIR) Spectroscopy. (2) ASTM D6348-03 Standard Test Method for Determination of Gaseous Compounds by Extractive Direct Interface Fourier Transform...

40 CFR 98.224 - Monitoring and QA/QC requirements.

Code of Federal Regulations, 2013 CFR

2013-07-01

... Inorganic Emissions by Extractive Fourier Transform Infrared (FTIR) Spectroscopy. (2) ASTM D6348-03 Standard Test Method for Determination of Gaseous Compounds by Extractive Direct Interface Fourier Transform...

Digital signal processing techniques for pitch shifting and time scaling of audio signals

NASA Astrophysics Data System (ADS)

Buś, Szymon; Jedrzejewski, Konrad

2016-09-01

In this paper, we present the techniques used for modifying the spectral content (pitch shifting) and for changing the time duration (time scaling) of an audio signal. A short introduction gives a necessary background for understanding the discussed issues and contains explanations of the terms used in the paper. In subsequent sections we present three different techniques appropriate both for pitch shifting and for time scaling. These techniques use three different time-frequency representations of a signal, namely short-time Fourier transform (STFT), continuous wavelet transform (CWT) and constant-Q transform (CQT). The results of simulation studies devoted to comparison of the properties of these methods are presented and discussed in the paper.

Use of the fractional Fourier transform in {pi}/2 converters of laser modes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Malyutin, A A

2004-02-28

The possibility of using the fractional Fourier transform (FrFT) in optical schemes for astigmatic {pi}/2 converters of Hermite-Gaussian modes to donut Laguerre-Gaussian modes is considered. Several schemes of converters based on the FrFT of the half-integer and irrational orders are presented. The lowest FrFT order than can be used in astigmatic mode converters is found. The properties of converters based on the fractional and ordinary Fourier transforms are compared. (laser beams)

Restoration algorithms for imaging through atmospheric turbulence

DTIC Science & Technology

2017-02-18

the Fourier spectrum of each frame. The reconstructed image is then obtained by taking the inverse Fourier transform of the average of all processed...with wipξq “ Gσp|Fpviqpξq|pq řM j“1Gσp|Fpvjqpξq|pq , where F denotes the Fourier transform (ξ are the frequencies) and Gσ is a Gaussian filter of...a combination of SIFT [26] and ORSA [14] algorithms) in order to remove affine transformations (translations, rotations and homothety). The authors

Tomography: Three Dimensional Image Construction. Applications of Analysis to Medical Radiology. [and] Genetic Counseling. Applications of Probability to Medicine. [and] The Design of Honeycombs. Applications of Differential Equations to Biology. Modules and Monographs in Undergraduate Mathematics and Its Applications Project. UMAP Units 318, 456, 502.

ERIC Educational Resources Information Center

Solomon, Frederick; And Others.

This document consists of three modules. The first looks at applications of analysis to medical radiology. The goals are to provide: 1) acquaintance with a significant applied mathematics problem utilizing Fourier Transforms; 2) generalization of the Fourier Transforms to two dimensions; 3) practice with Fourier Transforms; and 4) introduction to…

A laboratory demonstration of high-resolution hard X-ray and gamma-ray imaging using Fourier-transform techniques

NASA Technical Reports Server (NTRS)

Palmer, David; Prince, Thomas A.

1987-01-01

A laboratory imaging system has been developed to study the use of Fourier-transform techniques in high-resolution hard X-ray and gamma-ray imaging, with particular emphasis on possible applications to high-energy astronomy. Considerations for the design of a Fourier-transform imager and the instrumentation used in the laboratory studies is described. Several analysis methods for image reconstruction are discussed including the CLEAN algorithm and maximum entropy methods. Images obtained using these methods are presented.

Fast Fourier Transform algorithm design and tradeoffs

NASA Technical Reports Server (NTRS)

Kamin, Ray A., III; Adams, George B., III

1988-01-01

The Fast Fourier Transform (FFT) is a mainstay of certain numerical techniques for solving fluid dynamics problems. The Connection Machine CM-2 is the target for an investigation into the design of multidimensional Single Instruction Stream/Multiple Data (SIMD) parallel FFT algorithms for high performance. Critical algorithm design issues are discussed, necessary machine performance measurements are identified and made, and the performance of the developed FFT programs are measured. Fast Fourier Transform programs are compared to the currently best Cray-2 FFT program.

Depth-resolved dual-beamlet vibrometry based on Fourier domain low coherence interferometry

PubMed Central

Choudhury, Niloy; Chen, Fangyi; Wang, Ruikang K.; Jacques, Steven L.; Nuttall, Alfred L.

2013-01-01

Abstract. We present an optical vibrometer based on delay-encoded, dual-beamlet phase-sensitive Fourier domain interferometric system to provide depth-resolved subnanometer scale vibration information from scattering biological specimens. System characterization, calibration, and preliminary vibrometry with biological specimens were performed. The proposed system has the potential to provide both amplitude and direction of vibration of tissue microstructures on a single two-dimensional plane. PMID:23455961

Time history solution program, L225 (TEV126). Volume 1: Engineering and usage

NASA Technical Reports Server (NTRS)

Kroll, R. I.; Tornallyay, A.; Clemmons, R. E.

1979-01-01

Volume 1 of a two volume document is presented. The usage of the convolution program L225 (TEV 126) is described. The program calculates the time response of a linear system by convoluting the impulsive response function with the time-dependent excitation function. The convolution is performed as a multiplication in the frequency domain. Fast Fourier transform techniques are used to transform the product back into the time domain to obtain response time histories. A brief description of the analysis used is presented.

Fourier phase in Fourier-domain optical coherence tomography.

PubMed

Uttam, Shikhar; Liu, Yang

2015-12-01

Phase of an electromagnetic wave propagating through a sample-of-interest is well understood in the context of quantitative phase imaging in transmission-mode microscopy. In the past decade, Fourier-domain optical coherence tomography has been used to extend quantitative phase imaging to the reflection-mode. Unlike transmission-mode electromagnetic phase, however, the origin and characteristics of reflection-mode Fourier phase are poorly understood, especially in samples with a slowly varying refractive index. In this paper, the general theory of Fourier phase from first principles is presented, and it is shown that Fourier phase is a joint estimate of subresolution offset and mean spatial frequency of the coherence-gated sample refractive index. It is also shown that both spectral-domain phase microscopy and depth-resolved spatial-domain low-coherence quantitative phase microscopy are special cases of this general theory. Analytical expressions are provided for both, and simulations are presented to explain and support the theoretical results. These results are further used to show how Fourier phase allows the estimation of an axial mean spatial frequency profile of the sample, along with depth-resolved characterization of localized optical density change and sample heterogeneity. Finally, a Fourier phase-based explanation of Doppler optical coherence tomography is also provided.

40 CFR Appendix B to Subpart Uuuuu... - -HCl and HF Monitoring Provisions

Code of Federal Regulations, 2013 CFR

2013-07-01

... extractive Fourier Transform Infrared Spectroscopy (FTIR) continuous emissions monitoring systems in appendix... Fourier Transform Infrared (FTIR) Spectroscopy” (incorporated by reference, see § 63.14), each applied...

40 CFR 98.54 - Monitoring and QA/QC requirements.

Code of Federal Regulations, 2014 CFR

2014-07-01

... Inorganic Emissions by Extractive Fourier Transform Infrared (FTIR) Spectroscopy in 40 CFR part 63, Appendix... Direct Interface Fourier Transform Infrared (FTIR) Spectroscopy (incorporated by reference, see § 98.7...

40 CFR 98.54 - Monitoring and QA/QC requirements.

Code of Federal Regulations, 2011 CFR

2011-07-01

... Inorganic Emissions by Extractive Fourier Transform Infrared (FTIR) Spectroscopy in 40 CFR part 63, Appendix... Direct Interface Fourier Transform Infrared (FTIR) Spectroscopy (incorporated by reference, see § 98.7...

40 CFR 98.54 - Monitoring and QA/QC requirements.

Code of Federal Regulations, 2012 CFR

2012-07-01

... Inorganic Emissions by Extractive Fourier Transform Infrared (FTIR) Spectroscopy in 40 CFR part 63, Appendix... Direct Interface Fourier Transform Infrared (FTIR) Spectroscopy (incorporated by reference, see § 98.7...

40 CFR 98.54 - Monitoring and QA/QC requirements.

Code of Federal Regulations, 2013 CFR

2013-07-01

... Inorganic Emissions by Extractive Fourier Transform Infrared (FTIR) Spectroscopy in 40 CFR part 63, Appendix... Direct Interface Fourier Transform Infrared (FTIR) Spectroscopy (incorporated by reference, see § 98.7...

40 CFR Appendix B to Subpart Uuuuu... - -HCl and HF Monitoring Provisions

Code of Federal Regulations, 2014 CFR

2014-07-01

... extractive Fourier Transform Infrared Spectroscopy (FTIR) continuous emissions monitoring systems in appendix... Fourier Transform Infrared (FTIR) Spectroscopy” (incorporated by reference, see § 63.14), each applied...

Laboratory demonstration of a Brillouin lidar to remotely measure temperature profiles of the ocean

NASA Astrophysics Data System (ADS)

Rudolf, Andreas; Walther, Thomas

2014-05-01

We report on the successful laboratory demonstration of a real-time lidar system to remotely measure temperature profiles in water. In the near future, it is intended to be operated from a mobile platform, e.g., a helicopter or vessel, in order to precisely determine the temperature of the surface mixed layer of the ocean with high spatial resolution. The working principle relies on the active generation and detection of spontaneous Brillouin scattering. The light source consists of a frequency-doubled fiber-amplified external cavity diode laser and provides high-energy, Fourier transform-limited laser pulses in the green spectral range. The detector is based on an atomic edge filter and allows the challenging extraction of the temperature information from the Brillouin scattered light. In the lab environment, depending on the amount of averaging, water temperatures were resolved with a mean accuracy of up to 0.07°C and a spatial resolution of 1 m, proving the feasibility and the large potential of the overall system.

High-Resolution Mass Spectrometers

NASA Astrophysics Data System (ADS)

Marshall, Alan G.; Hendrickson, Christopher L.

2008-07-01

Over the past decade, mass spectrometry has been revolutionized by access to instruments of increasingly high mass-resolving power. For small molecules up to ˜400 Da (e.g., drugs, metabolites, and various natural organic mixtures ranging from foods to petroleum), it is possible to determine elemental compositions (CcHhNnOoSsPp…) of thousands of chemical components simultaneously from accurate mass measurements (the same can be done up to 1000 Da if additional information is included). At higher mass, it becomes possible to identify proteins (including posttranslational modifications) from proteolytic peptides, as well as lipids, glycoconjugates, and other biological components. At even higher mass (˜100,000 Da or higher), it is possible to characterize posttranslational modifications of intact proteins and to map the binding surfaces of large biomolecule complexes. Here we review the principles and techniques of the highest-resolution analytical mass spectrometers (time-of-flight and Fourier transform ion cyclotron resonance and orbitrap mass analyzers) and describe some representative high-resolution applications.

Optical spectroscopy and system-bath interactions in molecular aggregates with full configuration interaction Frenkel exciton model

NASA Astrophysics Data System (ADS)

Seibt, Joachim; Sláma, Vladislav; Mančal, Tomáš

2016-12-01

Standard application of the Frenkel exciton model neglects resonance coupling between collective molecular aggregate states with different number of excitations. These inter-band coupling terms are, however, of the same magnitude as the intra-band coupling between singly excited states. We systematically derive the Frenkel exciton model from quantum chemical considerations, and identify it as a variant of the configuration interaction method. We discuss all non-negligible couplings between collective aggregate states, and provide compact formulae for their calculation. We calculate absorption spectra of molecular aggregate of carotenoids and identify significant band shifts as a result of inter-band coupling. The presence of inter-band coupling terms requires renormalization of the system-bath coupling with respect to standard formulation, but renormalization effects are found to be weak. We present detailed discussion of molecular dimer and calculate its time-resolved two-dimensional Fourier transformed spectra to find weak but noticeable effects of peak amplitude redistribution due to inter-band coupling.

High-resolution Interferometer Sounder (HIS), phase 2

NASA Technical Reports Server (NTRS)

1988-01-01

The High-resolution Interferometer Sounder (HIS) was successfully built, tested, and flight proven on the NASA U-2/ER-2 high altitude aircraft. The HIS demonstration has shown that, by using the technology of Fourier Transform Spectroscopy (FTS), it is possible to measure the spectrum of upwelling infrared radiance needed for temperature and humidity sounding with high spectral resolution and high radiometric precision. By resolving individual carbon dioxide lines, the retrieved temperature profiles have vertical resolutions of 1 to 2 km and RMS errors less than 1 C, about 2 to 4 times better than possible with current sounders. Implementing this capability on satellite sounders will greatly enhance the dynamical information content of temperature measurements from space. The aircraft model HIS is now a resource which should be used to support field experiments in mesoscale meteorology, to monitor trace gas concentrations and to better understand their effects on climate, to monitor the surface radiation budget and the radiative effects of clouds, and to collect data for research into retrieval techniques, especially under partially cloudy conditions.

Förster resonance energy transfer studies of luminescent gold nanoparticles functionalized with ruthenium(II) and rhenium(I) complexes: modulation via esterase hydrolysis.

PubMed

Leung, Frankie Chi-Ming; Tam, Anthony Yiu-Yan; Au, Vonika Ka-Man; Li, Mei-Jin; Yam, Vivian Wing-Wah

2014-05-14

A number of ruthenium(II) and rhenium(I) bipyridine complexes functionalized with lipoic acid moieties have been synthesized and characterized. Functionalization of gold nanoparticles with these chromophoric ruthenium(II) and rhenium(I) complexes has resulted in interesting supramolecular assemblies with Förster resonance energy transfer (FRET) properties that could be modulated via esterase hydrolysis. The luminescence of the metal complex chromophores was turned on upon cleavage of the ester bond linkage by esterase to reduce the efficiency of FRET quenching. The prepared nanoassembly conjugates have been characterized by transmission electron microscopy (TEM), energy-dispersive X-ray analysis (EDX), Fourier transform infrared spectroscopy (FTIR), dynamic light scattering (DLS), UV-visible spectroscopy, and emission spectroscopy. The quenching mechanism has also been studied by transient absorption and time-resolved emission decay measurements. The FRET efficiencies were found to vary with the nature of the chromophores and the length of the spacer between the donor (transition metal complexes) and the acceptor (gold nanoparticles).

Battle Damage Assessment Using Inverse Synthetic Aperture Radar (ISAR)

DTIC Science & Technology

2004-12-01

are many forms of bilinear TFT. The most basic is the Wigner - Ville Distribution ( WVD ), which is defined as the Fourier transform of the time...resolution (compared to WVD — which is known (Chen [2]) to possess the best time-frequency resolution). Two well-known distributions in this category...resolution limit imposed by the STFT. Examples of some of these TFT schemes include the Continuous Wavelet Transform (CWT), the bilinear Wigner - Ville

Clustering change patterns using Fourier transformation with time-course gene expression data.

PubMed

Kim, Jaehee

2011-01-01

To understand the behavior of genes, it is important to explore how the patterns of gene expression change over a period of time because biologically related gene groups can share the same change patterns. In this study, the problem of finding similar change patterns is induced to clustering with the derivative Fourier coefficients. This work is aimed at discovering gene groups with similar change patterns which share similar biological properties. We developed a statistical model using derivative Fourier coefficients to identify similar change patterns of gene expression. We used a model-based method to cluster the Fourier series estimation of derivatives. We applied our model to cluster change patterns of yeast cell cycle microarray expression data with alpha-factor synchronization. It showed that, as the method clusters with the probability-neighboring data, the model-based clustering with our proposed model yielded biologically interpretable results. We expect that our proposed Fourier analysis with suitably chosen smoothing parameters could serve as a useful tool in classifying genes and interpreting possible biological change patterns.

Wavelet Filter Banks for Super-Resolution SAR Imaging

NASA Technical Reports Server (NTRS)

Sheybani, Ehsan O.; Deshpande, Manohar; Memarsadeghi, Nargess

2011-01-01

This paper discusses Innovative wavelet-based filter banks designed to enhance the analysis of super resolution Synthetic Aperture Radar (SAR) images using parametric spectral methods and signal classification algorithms, SAR finds applications In many of NASA's earth science fields such as deformation, ecosystem structure, and dynamics of Ice, snow and cold land processes, and surface water and ocean topography. Traditionally, standard methods such as Fast-Fourier Transform (FFT) and Inverse Fast-Fourier Transform (IFFT) have been used to extract Images from SAR radar data, Due to non-parametric features of these methods and their resolution limitations and observation time dependence, use of spectral estimation and signal pre- and post-processing techniques based on wavelets to process SAR radar data has been proposed. Multi-resolution wavelet transforms and advanced spectral estimation techniques have proven to offer efficient solutions to this problem.

40 CFR Appendix B to Subpart Uuuuu - -HCl and HF Monitoring Provisions

Code of Federal Regulations, 2012 CFR

2012-07-01

... Fourier Transform Infrared Spectroscopy (FTIR) continuous emissions monitoring systems in appendix B to... Fourier Transform Infrared (FTIR) Spectroscopy” (incorporated by reference, see § 63.14), each applied...

A fast discrete S-transform for biomedical signal processing.

PubMed

Brown, Robert A; Frayne, Richard

2008-01-01

Determining the frequency content of a signal is a basic operation in signal and image processing. The S-transform provides both the true frequency and globally referenced phase measurements characteristic of the Fourier transform and also generates local spectra, as does the wavelet transform. Due to this combination, the S-transform has been successfully demonstrated in a variety of biomedical signal and image processing tasks. However, the computational demands of the S-transform have limited its application in medicine to this point in time. This abstract introduces the fast S-transform, a more efficient discrete implementation of the classic S-transform with dramatically reduced computational requirements.

The Fourier Transform in Chemistry-NMR, Part 3. Multiple-Pulse Experiments.

ERIC Educational Resources Information Center

Williams, Kathryn R.; King, Roy W.

1990-01-01

Described are six multipulse experiments with an emphasis on their application to common problems in chemistry. Exercises in relaxation time measurement, spin echoes, and polarization transfer are proposed. (CW)

Time stretch dispersive Fourier transform based single-shot pulse-by-pulse spectrum measurement using a pulse-repetition-frequency-variable gain-switched laser

NASA Astrophysics Data System (ADS)

Furukawa, Hideaki; Makino, Takeshi; Wang, Xiaomin; Kobayashi, Tetsuya; Asghari, Mohammad H.; Trinh, Paul; Jalali, Bahram; Man, Wai Sing; Tsang, Kwong Shing; Wada, Naoya

2018-02-01

The time stretch dispersive Fourier Transform (TS-DFT) technique based on a fiber chromatic dispersion is a powerful tool for pulse-by-pulse single-shot spectrum measurement for highrepetition rate optical pulses. The distributed feedback laser diode (DFB-LD) with the gain switch operation can flexibly change the pulse repetition frequency (PRF). In this paper, we newly introduce a semiconductor gain-switched DFB-LD operating from 1 MHz up to 1 GHz PRF into the TS-DFT based spectrum measurement system to improve the flexibility and the operability. The pulse width can be below 2 ps with a pulse compression technique. We successfully measure the spectrum of each optical pulse at 1 GHz, 100 MHz, and 10 MHz PRF, and demonstrate the flexibility of the measurement system.

Nycterohemeral eating and ruminating patterns in heifers fed grass or corn silage: analysis by finite Fourier transform.

PubMed

Deswysen, A G; Dutilleul, P; Godfrin, J P; Ellis, W C

1993-10-01

Average daily and within-day nycterohemeral patterns of eating and ruminating behavior were determined in six Holstein-Friesian heifers (average BW = 427 kg) given ad libitum access to either corn or grass silage in a two-period crossover design. Rhythm components (number of cycles/24 h) were characterized by finite Fourier transform of the 24-h mastication activities as measured during 4 d by continuous jaw movement recordings. Average daily voluntary intake of corn silage was 8.2% greater (P = .05) than that for grass silage and was associated (P < .05) with fewer meals and shorter daily, unitary eating and ruminating times, and smaller number of rumination boli. Analysis of variance of the daily mean of hourly activities and Rhythm Components 1 to 12 indicated effects of (P < .05) silage type (S), animal (A), period (P), and a significant interaction (S x A x P) for each mastication activity. The finite Fourier transform was reparameterized to express the amplitude (as periodograms) and phase of each rhythm component. Rhythm Components 1, 3, and 4 contributed primarily to explaining the total dispersion of the 24-h series of time spent eating and ruminating, for both silage types and individual heifers. Relative importance of Rhythm Component 1 of time spent eating, indicative of a main circadian pattern, was related positively to pedigree value for milk production (P = .01) and negatively to milk protein concentration (P = .09).(ABSTRACT TRUNCATED AT 250 WORDS)

HIGH-RESOLUTION FOURIER TRANSFORM SPECTROSCOPY OF Nb i IN THE NEAR-INFRARED

DOE Office of Scientific and Technical Information (OSTI.GOV)

Er, A.; Güzelçimen, F.; Başar, Gö.

In this study, a Fourier Transform spectrum of Niobium (Nb) is investigated in the near-infrared spectral range from 6000 to 12,000 cm{sup −1} (830–1660 nm). The Nb spectrum is produced using a hollow cathode discharge lamp in an argon atmosphere. Both Nb and Ar spectral lines are visible in the spectrum. A total of 110 spectral lines are assigned to the element Nb. Of these lines, 90 could be classified as transitions between known levels of atomic Nb. From these classified Nb i transitions, 27 have not been listed in literature previously. Additionally, 8 lines are classified for the firstmore » time.« less

Experimental Research Into Generation of Acoustic Emission Signals in the Process of Friction of Hadfield Steel Single Crystals

NASA Astrophysics Data System (ADS)

Lychagin, D. V.; Filippov, A. V.; Novitskaia, O. S.; Kolubaev, E. A.; Sizova, O. V.

2016-08-01

The results of experimental research into dry sliding friction of Hadfield steel single crystals involving registration of acoustic emission are presented in the paper. The images of friction surfaces of Hadfield steel single crystals and wear grooves of the counterbody surface made after completion of three serial experiments conducted under similar conditions and friction regimes are given. The relation of the acoustic emission waveform envelope to the changing friction factor is revealed. Amplitude-frequency characteristics of acoustic emission signal frames are determined on the base of Fast Fourier Transform and Short Time Fourier Transform during the run-in stage of tribounits and in the process of stable friction.

Phase-shift detection in a Fourier-transform method for temperature sensing using a tapered fiber microknot resonator.

PubMed

Larocque, Hugo; Lu, Ping; Bao, Xiaoyi

2016-04-01

Phase-shift detection in a fast-Fourier-transform (FFT)-based spectrum analysis technique for temperature sensing using a tapered fiber microknot resonator is proposed and demonstrated. Multiple transmission peaks in the FFT spectrum of the device were identified as optical modes having completed different amounts of round trips within the ring structure. Temperature variation induced phase shifts for each set of peaks were characterized, and experimental results show that different peaks have distinct temperature sensitivities reaching values up to -0.542  rad/°C, which is about 10 times greater than that of a regular adiabatic taper Mach-Zehnder interferometer when using similar phase-tracking schemes.

Fourier transform infrared spectroscopy techniques for the analysis of drugs of abuse

NASA Astrophysics Data System (ADS)

Kalasinsky, Kathryn S.; Levine, Barry K.; Smith, Michael L.; Magluilo, Joseph J.; Schaefer, Teresa

1994-01-01

Cryogenic deposition techniques for Gas Chromatography/Fourier Transform Infrared (GC/FT-IR) can be successfully employed in urinalysis for drugs of abuse with detection limits comparable to those of the established Gas Chromatography/Mass Spectrometry (GC/MS) technique. The additional confidence of the data that infrared analysis can offer has been helpful in identifying ambiguous results, particularly, in the case of amphetamines where drugs of abuse can be confused with over-the-counter medications or naturally occurring amines. Hair analysis has been important in drug testing when adulteration of urine samples has been a question. Functional group mapping can further assist the analysis and track drug use versus time.

Autoregressive modeling for the spectral analysis of oceanographic data

NASA Technical Reports Server (NTRS)

Gangopadhyay, Avijit; Cornillon, Peter; Jackson, Leland B.

1989-01-01

Over the last decade there has been a dramatic increase in the number and volume of data sets useful for oceanographic studies. Many of these data sets consist of long temporal or spatial series derived from satellites and large-scale oceanographic experiments. These data sets are, however, often 'gappy' in space, irregular in time, and always of finite length. The conventional Fourier transform (FT) approach to the spectral analysis is thus often inapplicable, or where applicable, it provides questionable results. Here, through comparative analysis with the FT for different oceanographic data sets, the possibilities offered by autoregressive (AR) modeling to perform spectral analysis of gappy, finite-length series, are discussed. The applications demonstrate that as the length of the time series becomes shorter, the resolving power of the AR approach as compared with that of the FT improves. For the longest data sets examined here, 98 points, the AR method performed only slightly better than the FT, but for the very short ones, 17 points, the AR method showed a dramatic improvement over the FT. The application of the AR method to a gappy time series, although a secondary concern of this manuscript, further underlines the value of this approach.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Laskin, Julia

In this work, resonant ejection coupled with surface-induced dissociation (SID) in a Fourier transform ion cyclotron resonance mass spectrometer is used to examine fragmentation kinetics of two singly protonated hexapeptides, RYGGFL and KYGGFL, containing the basic arginine residue and less basic lysine residue at the N-terminus. The kinetics of individual reaction channels at different collision energies are probed by applying a short ejection pulse (1 ms) in resonance with the cyclotron frequency of a selected fragment ion and varying the delay time between ion-surface collision and resonant ejection while keeping total reaction delay time constant. Rice-Ramsperger-Kassel-Marcus (RRKM) modeling of themore » experimental data provides accurate threshold energies and activation entropies of individual reaction channels. Substitution of arginine with less basic lysine has a pronounced effect on the observed fragmentation kinetics of several pathways, including the b2 ion formation, but has little or no effect on formation of the b5+H2O fragment ion. The combination of resonant ejection SID, time- and collision energy-resolved SID, and RRKM modeling of both types of experimental data provides a detailed mechanistic understanding of the primary dissociation pathways of complex gaseous ions.« less

An Evaluation of the Environmental Fate and Behavior of Munitions Materiel (Tetryl and Polar Metabolites of TNT) in Soil and Plant Systems. Environmental Fate and Behavior of Tetryl

DTIC Science & Technology

1992-03-01

attempted to verify product identity and purity by GC with either Fourier transform infrared spectro.icopy (FTIR) or mass spectroscopy (MS) detection...ýl0 5 In-1 z U)-’i0oo -3g’i o -6o0 626o a i60 ito1 2i oo I ’ o [JfnVENUII8ER (cm- FIGURE 3,9. Fourier Transform Infrared Spectroscopy Spectrum of...Fourier Transform Infrared Spectroscopy Spectrum of Tetryl I-I F1U~IGUR Fourier Utransformlfret Spcrop S ectrum of TeasomtinPoutrl 0 , -39 i : : : -. . i

Fourier resolved spectroscopy of 4U 1543-47 during the 2002 outburst

NASA Technical Reports Server (NTRS)

Reig, P.; Papadakis, I. E.; Shrader, C. R.; Kazanas, D.

2006-01-01

We have obtained Fourier-resolved spectra of the black-hole binary 4U 1543-47 in the canonical states (high/soft, very high, intermediate and low/hard) observed in this source during the decay of an outburst that took place in 2002. Our objective is to investigate the variability of the spectral components generally used to describe the energy spectra of black-hole systems, namely a disk component, a power-law component attributed to Comptonization by a hot corona and the contribution of the iron line due to reprocessing of the high energy (E greater than or approx, equal to 7 keV) radiation. We find that i) the disk component is not variable on time scales shorter than approx. 100 seconds, ii) the reprocessing emission as manifest by the variability of the Fe K(alpha) line responds to the primary radiation variations down to time scales of approx. 70 ms in the high and very-high states, but longer than 2 s in the low state, iii) the low-frequency QPOs are associated with variations of the X-ray power law spectral component and not to the disk component and iv) the spectra corresponding to the highest Fourier frequency are the hardest (show the flatter spectra) at a given spectral state. These results questions the models that explain the observed power spectra as due to modulations of the accretion rate only.

Collision cross section (CCS) measurement by ion cyclotron resonance mass spectrometry with short-time Fourier transform.

PubMed

Hu, Miao; Zhang, Linzhou; He, Shan; Xu, Chunming; Shi, Quan

2018-05-15

The collision cross section (CCS) is an important shape parameter which is often used in molecular structure investigation. In Fourier transform ion cyclotron resonance mass spectrometry (FTICR-MS), the CCS affects the ion signal damping shape due to the effect of ion-neutral collisions. It is potential to obtain ion CCS values from FTICR-MS with the help of a proper ion-collision model. We have developed a rapid method to obtain the ion damping profile and CCS for mixtures by only one FTICR-MS measurement. The method utilizes short-time Fourier transform (STFT) to process FTICR-MS time domain signals. The STFT-processed result is a three-dimensional (3D) spectrum which has an additional time axis in addition to the conventional mass-to-charge ratio and intensity domains. The damping profile of each ion can be recognized from the 3D spectrum. After extracting the decay profile of a specified ion, all the three ion-neutral collision models were tested in curve fitting. The hard-sphere model was proven to be suitable for our experimental setup. A linear relationship was observed between the CCS value and hard-sphere model parameters. Therefore, the CCS values of all the peaks were obtained through the addition of internal model compounds and linear calibration. The proposed method was successfully applied to determine the CCSs of fatty acids and polyalanines in a petroleum gas oil matrix. This technique can be used for simultaneous measurement of cross sections for many ions in congested spectra. Copyright © 2018 John Wiley & Sons, Ltd.

Polynomial Phase Estimation Based on Adaptive Short-Time Fourier Transform

PubMed Central

Jing, Fulong; Zhang, Chunjie; Si, Weijian; Wang, Yu; Jiao, Shuhong

2018-01-01

Polynomial phase signals (PPSs) have numerous applications in many fields including radar, sonar, geophysics, and radio communication systems. Therefore, estimation of PPS coefficients is very important. In this paper, a novel approach for PPS parameters estimation based on adaptive short-time Fourier transform (ASTFT), called the PPS-ASTFT estimator, is proposed. Using the PPS-ASTFT estimator, both one-dimensional and multi-dimensional searches and error propagation problems, which widely exist in PPSs field, are avoided. In the proposed algorithm, the instantaneous frequency (IF) is estimated by S-transform (ST), which can preserve information on signal phase and provide a variable resolution similar to the wavelet transform (WT). The width of the ASTFT analysis window is equal to the local stationary length, which is measured by the instantaneous frequency gradient (IFG). The IFG is calculated by the principal component analysis (PCA), which is robust to the noise. Moreover, to improve estimation accuracy, a refinement strategy is presented to estimate signal parameters. Since the PPS-ASTFT avoids parameter search, the proposed algorithm can be computed in a reasonable amount of time. The estimation performance, computational cost, and implementation of the PPS-ASTFT are also analyzed. The conducted numerical simulations support our theoretical results and demonstrate an excellent statistical performance of the proposed algorithm. PMID:29438317

Polynomial Phase Estimation Based on Adaptive Short-Time Fourier Transform.

PubMed

Jing, Fulong; Zhang, Chunjie; Si, Weijian; Wang, Yu; Jiao, Shuhong

2018-02-13

Polynomial phase signals (PPSs) have numerous applications in many fields including radar, sonar, geophysics, and radio communication systems. Therefore, estimation of PPS coefficients is very important. In this paper, a novel approach for PPS parameters estimation based on adaptive short-time Fourier transform (ASTFT), called the PPS-ASTFT estimator, is proposed. Using the PPS-ASTFT estimator, both one-dimensional and multi-dimensional searches and error propagation problems, which widely exist in PPSs field, are avoided. In the proposed algorithm, the instantaneous frequency (IF) is estimated by S-transform (ST), which can preserve information on signal phase and provide a variable resolution similar to the wavelet transform (WT). The width of the ASTFT analysis window is equal to the local stationary length, which is measured by the instantaneous frequency gradient (IFG). The IFG is calculated by the principal component analysis (PCA), which is robust to the noise. Moreover, to improve estimation accuracy, a refinement strategy is presented to estimate signal parameters. Since the PPS-ASTFT avoids parameter search, the proposed algorithm can be computed in a reasonable amount of time. The estimation performance, computational cost, and implementation of the PPS-ASTFT are also analyzed. The conducted numerical simulations support our theoretical results and demonstrate an excellent statistical performance of the proposed algorithm.

A Step-by-Step Picture of Pulsed (Time-Domain) NMR.

ERIC Educational Resources Information Center

Schwartz, Leslie J.

1988-01-01

Discusses a method for teaching time pulsed NMR principals that are as simple and pictorial as possible. Uses xyz coordinate figures and presents theoretical explanations using a Fourier transformation spectrum. Assumes no previous knowledge of quantum mechanics for students. Usable for undergraduates. (MVL)

Synthesis, Analysis, and Processing of Fractal Signals

DTIC Science & Technology

1991-10-01

coordinator in hockey, squash, volleyball, and softball, but also for reminding me periodically that 1/f noise can exist outside a computer. More...similar signals as Fourier-based representations are for stationary and periodic signals. Furthermore, because wave- let transformations can be...and periodic signals. Furthermore, just as the discovery of fast Fourier transform (FFT) algorithms dramatically increased the viability the Fourier

AN INTEGRATED MODEL FOR THE PRODUCTION OF X-RAY TIME LAGS AND QUIESCENT SPECTRA FROM HOMOGENEOUS AND INHOMOGENEOUS BLACK HOLE ACCRETION CORONAE

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kroon, John J.; Becker, Peter A., E-mail: jkroon@gmu.edu, E-mail: pbecker@gmu.edu

2016-04-20

Many accreting black holes manifest time lags during outbursts, in which the hard Fourier component typically lags behind the soft component. Despite decades of observations of this phenomenon, the underlying physical explanation for the time lags has remained elusive, although there are suggestions that Compton reverberation plays an important role. However, the lack of analytical solutions has hindered the interpretation of the available data. In this paper, we investigate the generation of X-ray time lags in Compton scattering coronae using a new mathematical approach based on analysis of the Fourier-transformed transport equation. By solving this equation, we obtain the Fouriermore » transform of the radiation Green’s function, which allows us to calculate the exact dependence of the time lags on the Fourier frequency, for both homogeneous and inhomogeneous coronal clouds. We use the new formalism to explore a variety of injection scenarios, including both monochromatic and broadband (bremsstrahlung) seed photon injection. We show that our model can successfully reproduce both the observed time lags and the time-averaged (quiescent) X-ray spectra for Cyg X-1 and GX 339-04, using a single set of coronal parameters for each source. The time lags are the result of impulsive bremsstrahlung injection occurring near the outer edge of the corona, while the time-averaged spectra are the result of continual distributed injection of soft photons throughout the cloud.« less